Funny you should ask.
I am not replacing the M41 yet. There's simply no need at the present time, as it's still a better tank in almost all respects than Peru's Panzer IVs. However, I will be rebuilding them with new engines and turrets, which was a refit planned from the inception of the design. A replacement is planned for sometime in the 1946 to 1948 period.
What is Chile's doctrine in general because Peru's is at least for now defensive in nature (at least in RL)
That requires a bit of a twofold answer, but I'm glad you asked since the doctrine and the history of the Chilean Army in Wesworld feeds a few of the developments above (particularly in regards to the Armoured Cavalry).
In brief, Chile's doctrine emphasizes a war of attack and maneuver across a battlespace, in accordance with the German, Russian, and French doctrines taught in the Chilean Army staff schools. Since Chile's army is smaller than that of its neighbors (except Bolivia, who's army size is limited to two divisions by the Bogota Treaty), the doctrine is to maintain a professional and mobile force.
In terms of capability, Argentina is Chile's greatest threat due to their very large and increasingly mechanized army, and their possession of a very long border. In terms of intentions, however, Argentina is a very minimal threat since they're allies and partners, and threatened by much greater enemies on other borders. Bolivia's intentions, by contrast, are hostile and likely to become more so in the future - but their capabilities are, at the moment, quite limited because of treaty limitations and a lack of supporting arms. Finally, Peru has exhibited hostile intentions in the past - using aggresive diplomacy during the Andean War to recover Tacna, attempting to turn Bolivia into a puppet state, and invading Colombia. While this largely ended with the current regime, Chile sees Peru as highly unstable. In terms of capabilities, Peru has a bit of a mixed bag; the Chileans highly regard their current navy after the last five years of acquisitions, but the Peruvian Air Force and Army are perceived as lower or mixed quality.
Most of the senior command leadership in the Chilean Army are veterans of the early 1930s Andean War, which saw Chile invaded by Bolivia. A major early defeat resulted in Chilean forces operating at a heavy numeric imbalance during the first year of the war, during which time Chilean forces practiced an extended campaign of maneuver warfare - albeit with only limited mechanization - against the invading Bolivian army, as advised by Chile's foreign (German, Atlantean, and Russian) advisors. On the occasions where Chile rested on the defense or allowed static Great War like conditions to occur, friendly casualties went up, enemy casualties went down, and a general state of dismay followed.
The Chilean Army was in the midst of a rearming cycle in 1937 when the Peruvian War started. Since the Peruvian troops on the southern border pretty quickly declared for the Congressionalists, the Chilean Army didn't see much action, aside from the Titicaca Campaign, where a makeshift armour and infantry force ejected the Peruvian Army from western Bolivia. (In most ways, the campaign was less of combat problem and more of a logistical exercise.) That pretty much served to validate Chile's opinions on mobile warfare.
Overall, those experiences have led the Chilean Army to adopt a doctrine of maneuver and attack; and the methodology of how that doctrine takes shape is through moderately-sized combined-arms battlegroups. In the Andean War and then the Titicaca Campaign, these battlegroups were improvisational, ranging from battalion to regimental size. With this 1944 reorganization, these combined-arms units shall no longer be ad hoc affairs. On the brigade level, the Chilean Army now has the two Panzergrenaderos Brigades, which mix the vital combined arms (tanks, mechanized infantry, and artillery) in one dedicated package. And now on a smaller level, the Chilean Army has the two Armoured Cavalry Brigades, with a total of eight combined-arms units on the battalion level.
In theory, a similar doctrine could be used on a higher (divisional) level as well - for instance, creating a full Armoured Division - but the Chilean Army really doesn't think this is suitable for the South American situation. The terrain is the main issue preventing this: the logistics of maneuvering an armoured division are simply immense, and the relative scarcity of roads on the Chilean frontiers mean that large forces are going to be dependent on arteries of fixed and finite capacity. Lest anyone doubt... the Chilean Panzergrenaderos Brigade requires a total of 495 light and medium trucks, 78 scout cars, 193 half-tracks, and 282 staff cars or jeeps. Each of the 4,500 fighting men requires between 25 to 100 pounds (11 to 45 kilos) of supplies per day (food, water, medicine, ammunition, fuel, spare parts...). Let's call it 50 pounds / 22.7 kg per man, which is probably a low figure for a mechanized formation. That means a 4,500-man force requires 102,150 kilos (102 metric tons) of supplies per day in order to remain in the field, not even necessarily in combat conditions. Now imagine supplying this brigade using only a one-track dirt road in the Atacama or the Andes. Triple or quadruple this figure to imagine what chaos an armoured division would cause to the supply chain! In short, Chile feels larger armoured formations will simply be too complex.
With all that said, I'd note that the large majority of the Chilean Army remains as unmechanized, lightly-motorized infantry. By this, I mean that the infantry's supporting arms (artillery, mortars, and supply troops) have sufficient trucks to move all their gear and supplies, but the infantry troops themselves can only move as fast as a man can walk, and strategic movements must be carried out either by ship or rail. (The Fuerza Aerea de Chile has transport aircraft, but this is sufficient only to move small formations at relatively greater expense. Air mobility is used only when speed triumphs over considerations of economy.) The infantry regiments, which I detail above, are designed mainly to act in the situations where the combined-arms groups have some disadvantage, for instance in extreme mountainous conditions like the Andes, built-up regions such as cities, or heavy overgrowth regions such as the Bolivian jungles or the southern temperate rainforests. Additionally, they provide mobile formations a partner which is superior at standing on a piece of ground and controlling it absolutely. At least some of the reinforced infantry regiments, by the way, are maintained as reserve formations - they have a full-time cadre of the professional services (artillery, engineers, etc) but many of the units are composed of reservists who only serve a few weeks per year, or conscripted men who will only be in the uniform for about two years before moving to the reserves.
Going back to doctrine, there's one element I haven't touched on - counterinsurgency. As a result of the political treaties which ended the Andean War, Chile has obtained control of a very large slice of southwestern Bolivia, with a population of (if I recall correctly) about 1.6 million people. This region was originally quite restive as a result of guerrillas operating in the population, but the Chilean Army practiced a successful counterinsurgency campaign from 1934 to 1936. The region remains under Chilean control as the Chilean Bolivia Special Administrative Region, with a locally-recruited paramilitary force backed by the Chilean Army (specifically the infantry arm). In brief, the Chileans have focused on several main strategies. First, they use their troops to create safe zones where guerrilla activity is made nearly impossible. Second, they raise up cooperative local leaders within these areas in order to establish a friendly collaboration, encouraging them by providing prosperity and security. Third, they expand their zone of control by degrees to bring in outlying settlements, driving rebels further back into the hinterlands and depriving them of support. Fourth, they engage and defeat any diehard rebel bands.
Overall, these efforts have largely succeeded. In conjunction with infrastructure development programs, the CBSAR now has a GDP per capita about twice that of the Republic of Bolivia, and has been quiescient for several years, now. The vast majority of incidents stem not from homegrown rebels, but from "freedom fighters" supported secretly by the Bolivian government, crossing the border into the CBSAR - where they are strenuously opposed by CBSAR troops supported by a few Chilean Army formations.