Milk alternatives???

Little background:

My daughter is a year old, her main food source was formula. I then started mixing in a little bit of whole milk, no more than 4oz at a time and she also ate a few bites off our plates during meal times. About 2 weeks ago, my SO gave her 8oz of pure whole milk and then she started having a crazy amount of diarrhea for 5 days straight. We were changing her 2-3 in one hour sometimes. We were finally able to get her into the doctor (SO took her). Doctor advised us to cut out all dairy from her diet which includes formula. After a few days of no dairy, her stools started getting better but im having the hardest time keeping her fed. Shes now refusing to eat off our plate or even her own plate when i make her stuff. Im giving her Pedialyte, gerber puree pouches, baby cookies and water. She wont really eat anything else. Both her dad and I are lactose intolerant so i bought lactose free whole milk and gave her 4oz at bedtime yesterday and another 4oz today at nap time. Now her stools are starting to look more like diarrhea again so im assuming she really does have a problem with dairy.

My question is for those of you who have kids that cant handle dairy, what alternatives do you give them? Lactose free didnt work, should i try coconut milk? Almond milk? Soy milk? Has anyone given their LO those nutritional shakes for toddlers as a milk alternative? My daughter used to want a bite out of anything we were eating but now she almost runs away from us when we try to feed her real food. If we let her feed herself, she just plays with thw food. Any ideas on how to get this child fed?