OP, what area do you live in? You might find a provider here who would accommodate that allergy.

I think the other thing to consider is that a lot of providers will accommodate an allergy that is not life-threatening. They would do their best to make sure your child does not consume dairy but, in daycare, unless the entire daycare environment is dairy-free there could be transfer from one small set of hands to another. KWIM?

I accommodate allergies to a point; if they are epi-pen, anaphylaxis type allergies then, sorry, but that is WAY too big a risk for me to accept.

Just be very upfront with the provider so you can ensure she is really on board.