Milk allergies and Lactose intolerance are separate issues, though they don't have to be mutually exclusive. The first thing I would do, in your shoes, is to shop for a new pediatrician who is a little more educated about humans drinking cow's milk!!
My baby (now 16 months) had horrible reflux and was unable to digest Casein as well. I discovered this at 3 months and cut dairy from my diet (breastfeeding as well) and the reflux completely went away. Now that she is starting table food, she also reacts to soy, but with a rash. Many people who have dairy allergies also have soy (and sometimes corn) allergies.
I have a recipe and spreadsheet, etc for a hypo-allergenic formula that you can make that has all of the needed fat and vitamins, etc without using soy. It uses coconut milk, hemp milk, and flax oil. It is from a homeopathic pediatrician. If you would like it or more info, feel free to message me with your email address and I will send it.
Breastfeeding is still the best thing you can do! Can you make her cereal with pumped milk, rice milk, hemp, or coconut milk instead? OR just skip the cereal and give her babyfood. We personally delayed solids until she absolutely hit all of the markers to eat, and then she wasn't interested. Now e know it's because of all her various allergies most likely, but she is a good eater at 16 months.
Hope this helps! Let me know if you want more info!
Amanda