It really depends on the age of the child. With the proliferation of perverts the child would have to be 7 or 8 before I would allow them to go alone. Then I would be holding the door open so I could hear if something was wrong.
For your particular case it would depend on how big the bathroom and where the urnials were. If there were stalls that he could get to without the child being exposed to men at urnials then I guess he could take her to the mens room. If not then I would have him knock on the womens room door and announce his coming in with his daughter. Then he should enlist a woman's aid in making sure that anyone coming knows that he is there. I would not trust my child to a stranger no matter who there are you just don't know what they will do.
