I haven't sailed Princess in a while and my allergies are different from yours, but I was watching videos on YouTube and they showed a whole section of gluten-free pastries and muffins at breakfast and at least one gluten-free dessert was shown each day. Every cruise I have been on they recommend that you not eat in the buffet if you have allergies, but mine are mostly annoyances, not life threatening. At the buffet, someone can get a chef to help you with ingredient info. I'm sure there is at least one non-dairy "milk" on board, but if you want a specific brand or type, I would recommend bringing your own. Although this is a really old email address, you can and reach out to dietaryrequest@princesscruises.com with your questions.