It really depends on your daughter. My son, who is very highly allergic to milk and reacts if he has even 1-2 bites of something with milk in it, does not have a problem with things processed in the same facility or on shared equipment.
Generally, the proteins in milk that kids are allergic to do not transfer through the air the same way nut proteins do. In most cases, shared facilities and/or equipment will not cause a reaction for a milk allergy.
I'd consult with your doctor to be sure, or at least try only a very small amount the first time you give something that says that on the label.