My son had a few issues when we transitioned to whole milk as well. He had diaper rash, loose poop, and gas. He always had to be on soy formula because he had issues with milk based formulas. He was able to tolerate small doses of dairy from about 9 months like your little girl, so i really assumed the milk-based issue had been worked through.
We put him on Lactaid for a couple months. it's much more pricey than regular whole milk, but we were able to switch him to regular whole after that. I'm not sure if your daughter is having issues with the lactase but this seemed to work for my guy until he got better acclimated to the larger amounts of dairy.
It's worth a try anyway... i was tempted to give him soy milk (Silk) but there wasn't any that i could find with the same fat content... and ultimately that's why they keep them on whole milk as a follow up to formula/breastmilk. Edit: I did speak with my pediatrician about using Soy milk, and she frowned upon it and recommended toddlers stay away from it unless it's absolutely necessary. See what your ped. thinks before you make the change to Soy Milk.
good luck to you... it's worth a try.