Sensitive stomach/vomiting...?

Hi, I have a little female Shetland Sheepdog that I adopted, 6 months old this week, and she is very dainty and small. She's healthy and just got spayed. I haven't had her very long. Here is the problem - she seems to have a very sensitive stomach. I have her on IAMS Smart Puppy kibble and she eats that but occasionally has diarrhea, and I notice whenever I feed her certain meats like red meats or hot dogs or steak, she ends up vomiting. I don't know why. She seems fine with light, white meats like bits of turkey and chicken, and if I feed her any dog treats, it seems like it has to be the expensive, all natural, meat as first ingredient stuff or she vomits. Do you think this is serious enough to contact her vet about, or is it a simple case of a tender tummy? Can any of you recommend a good brand puppy food for sensitive stomachs?