Like other posters have mentioned, altitude has different effects on different people. I'm not a doctor, but I'm not sure it's a good idea to bring an infant from (presumably) 500 ft in RIX to 12,500 feet in JUL/Puno. It seems like too much risk for a 3 month old, especially with unknown lung strength and a multitude of other factors.
When traveling to these places with 12 yr olds, we started in CUZ, then went to Puno. If/when you decide to go, I definitely recommend working your way up in elevation.