"Upgrade" is in the eye of the beholder. And learning to shoot fast-moving wildlife is not a skill you pick up overnight. Even with the gear. I would also point out that the Canon dSLR bodies tier by the number of digits in their model designation. A XXXXD is actually a downgrade from an XXXD, if you're looking at cameras in the same processor/sensor generation. In some ways, the 1200D is a downgrade from the 350D (e.g., it doesn't have an IR sensor for the Canon wireless shutter remotes).
I would also say that I was perfectly capable of shooting bird-in-flight shots with a 350D--after I bought an EF 400mm f/5.6L USM and had been trying to get bird-in-flight shots for about two years. But probably an XXD or 7D body would be a better choice for serious wildlife shooting, because of the more sophisticated AF system and higher burst rate.
My recommendation would be to consider renting one of these bodies and a supertelephoto lens (say, a 100-400L, or one of the Sigma 400mm or 500mm lenses), and getting a monopod or tripod. And getting it early and practicing like hell before the trip. Unless your partner plans on shooting wildlife as a regular thing, this sounds more like a special-occasion lens that's only going to be used the once, and a rental is going to cost a lot less than purchasing the lens and camera body together.