The XP just tracks pregnancy progress - this game doesn't have a typical level-up system. Instead, each successful birth improves your stats like a level up would.
In other words, you have to be pregnant to gain "levels" - which means you need to craft and absorb a class crystal. You'll get plenty of materials to do so, but the bottleneck I ran into was gold; make sure you always have either a fresh crystal, or the money to make one, in your inventory.