Kudos to you! I'm impressed with how responsible you and your girlfriend are being.
Since the prescription information on the most common type of birth control pill (combination oral contraceptive) doesn't say anything about milk allergies, I would think it would be okay for her. Some women do have side effects, and it is best if she doesn't smoke but most women don't have side effects from the pill and will actually have some pleasant effects - such as a shorter, lighter period.
Your girlfriend will need to see a doctor to get a prescription and it is important that she get a .P.A.P exam annually now that she is becoming sexually active. When she goes to the doctor for the prescription she can ask about her milk allergy just to be certain.
Condoms and/or spermacides can be used as extra backup, especially as she is still getting accustomed to taking a pill at the same time every day. Backup is also needed for the first week of her first pack of pills. Condoms alone can work, but are less effective than hormonal methods especially when you consider the human-error effect.