No matter if you are married or not the baby will be entitiled to become British and carry a British passport. Make sure you can satify the criteria for the C2 form, there are other threads on the forum relating to baby passports so take a look at them with the search facility.
Make sure your fiancee keeps all her scan photos and paperwork from the doctor and hospital, plus all birth registration papers, receipts for meds in the hospital etc etc. The British Embassy recommended that we register our son's birth by applying for his passport as soon as we could after his birth. You do not need to get your baby a British birth certificate your official NSO cert is enough. We applied for our son at 5 weeks old. After application, we recieved his British passport 4 weeks later.
