I didn't see your previous post or I'd have said, yes, stick with that size for a while. For a young BP to go so quickly from eating next to nothing to eating a large
mouse might be a digestive challenge...let's hope he keeps it down. Not that they have such choices in the wild though, & it's mostly fine.
I would stick w/ medium (NOT large) mice for some time, actually...if he was my snake. It's better not to push it too far...it's too soon to rush to a small rat.
But also, as sufficio's post suggested, rat fuzzies or rat pups would also be fine...they're about the same size as the med. mouse...so either way.
If nothing else, snakes teach us patience...