My husband and I are thinking if we should just combine our baby's baptism and first birthday celebration. Do you think that will be fine?

Practically speaking, yes that's fine. It will save you a lot of money, time, effort. I've witnessed lots of friends doing the same and I felt that it's just as great! :) I actually thought of doing the same thing but my parents who are very traditional and thinks that baby would be 'too big enough' on a baptismal gown and that they prepare her on a plane trip (which they think is better, "safer" to take if baby is baptised before hand) we had her Christening roughly 3 months before her 1st birthday. Later on hubby and I realised that it could have been wiser for us to just combine it so we had more money left for savings.