Hi! I have been a vegan for almost 4 years and go on as many cruises as I can. I have cruised with NCL, Disney, and RC. NCL is AWESOME with vegan options.
1. Embarkation day have your daughter go to the main dining room and ask to speak to the Maitre D or asst Maitre D. If you are planning on eating in the MDR, NCL has a separate vegan menu that she can select her dinner options. If the rush of embarkation day is too much, simply do it at dinner; but she runs the risk of not being able to order from the special vegan menu until the next day (they let me, but I think it was an exception to the rule).
2. Upon sitting down in any dining space, the wait staff will always ask "Is there any dietary restrictions?" I found the staff on NCL Breakaway and NCL Escape well trained in knowing options for vegans.
3. Buffet - ton of options. If she has a question, just ask. The staff is amazing showing what is vegan. In fact on the Breakaway I asked one staff member behind the line a question on how something was prepared on a busy lunch rush. He pulled me to the front of the line in the front part of the buffet. And was showing me all these awesome salads and hummus options for me.
4. Specialty restaurants are a little hard. But they will go above and beyond. NO Vegan Options at Le Bistro (its French - butter, cream, cheese). This is my husband and daughters fav specialty = but never a problem. I always just eat a big lunch and grab something at the buffet either before or after dinner.
No one on NCL has ever made me feel like I am a problem or issue. I never go hungry and I feel that NCL has only gotten better over the years.
If you are traveling to Mr. Sanchos (Cozumel) or Maya Chan (Costa Maya) (beach clubs) both have vegan menus.
Hope this helps.