Since your fiance has higher earnings, he might benefit more from claiming a dependent. However, it depends on your exact circumstances. You can prepare your separate returns with each of you claiming your child as a dependent to see what the outcome would be.
Prior to actually filing your returns, you can enter whatever information you need to in order to determine the best approach for filing your tax returns. However, once you decide how you are going to file your returns, you want to make sure that the information in the system has been updated to reflect how you are going to file.