You´ll have mix weather
I think you would have dry climate up to southern Peru.
In northern Andean Peru (as in Chachapoyas) by November…., you would have already rains, but how much……, it will depend of every specific year.
Ecuador and Colombia by December….., make sure your gear is waterproof: it’s our rainy season by excellence. Some years it is mild, others heavy, meaning it rains every day, especially in the afternoon.
Otherwise, (you are asking for alternate suggestions), running your trip in the opposite direction, by mid-September rains would start in Colombia (usually mild), some rains in Ecuador but not “rainy-season”, dry high-Andes and northern Chile, and scorching and humid after Mendoza to Buenos Aires by December.
Enjoy our continent !!