This is the setup I have in my house ... well, with a different printer (a Brother) and an Airport Extreme Basestation. I've had a setup like this (with an HP printer at one point) in my house for a long time. You're not going to like what I'm about to say.
Some printers just don't work in this configuration because they don't have the software to handle it. Period. No amount of wishing or fiddling will change that.
I learned this the hard way over the course of 2 days and about 14 hours of fiddling, searching, etc., with a Samsung printer. The model we had picked up just wouldn't work plugged directly into the router. That's when we got the Brother multifunction laser printer we have now.
Sorry to be the bearer of bad news. On the positive side of things, this gives you the perfect excuse to get an even better printer.

Just be sure to search the Apple website first to make sure it'll work with your APE.