The rash around her mouth sounds like an allergic reaction. DD1 is allergic to dairy (and soy, and eggs). We introduced yogurt around 11 months, and she'd get red around her mouth. Then when we gave her cheese, she'd get hives where it touched her skin. At her 1 yr check up, I told the pedi about those reactions, and she ordered a blood RAST test to check for allergies. Her numbers were really high for dairy and egg, so we were prescribed Epipens to have on hand (we've thankfully never had to use them).
Anyway, we were able to just cut obvious dairy and egg from her diet. She can handle dairy and eggs if they're cooked into foods like bread, crackers, etc. She just can't have yogurt, cheese, ice cream, butter, sour cream, milk, or eggs by themselves.
I would talk to the pedi and ask for a RAST test. You can also see a pediatric allergist for a skin test and for more info.