Your snake can definitely move up in prey size. Most BPs can start on hoppers right out of the egg and move up to adult mice after only a few meals. Another advantage to moving up in size is that while it can be hard for a store to keep babies of the appropriate sizes in stock (can't always control when a mouse will have a litter), they should always have adults in stock.

I wouldn't worry too much about the snake eating the live fuzzy. They seem to have some understanding of when a prey item is too small/weak to hurt them, and will sometimes choose to skip the whole constriction step to save energy I suppose.