Remember, too, that rats are technically nocturnal (although mine have always seemed to live more by the "catnaps off and on throughout the day and night" rule). It could be that your baby is a hyper little monkey during the night while you're sleeping!

I currently have 5 boys, 4 of whom are around 2 to 3 months old, and they all demonstrate different levels of activity/sleepiness. A vet check might be a good idea if you're concerned, but it's probably nothing to worry about.