The smallest filter I've seen is the Red Sea Nano filter. It's good for up to about 3 gallons, and it's got an adjustable output. It's made to attach to a straight tank wall though, so I'm not sure if it would fit a bowl. Also, not sure if it would fit since you have a cover on the bowl.
There's also an Elite submersible mini filter for up to 3 gallons which would likely fit if you have a gap in the cover for the power cord, but it might take up a bit of space inside the bowl.