I don't know if that model of router will do this or not, but you're correct. You do not want to put that outside. You will want to buy a model that allows you to unhook those little black antennas, and hook up a cable. This cable would then have to get run outside, to an antenna mounted on the roof of your building.
I'm currently at work, so I don't have a whole lot of time to find these products for you, but I'll do some looking a little later to give you a better idea of what I'm talking about.
Edit: Here's a link to a wireless antenna that should work for you.
http://www.hyperlinktech.com/web/hgv-2404_06_09U.php
I'm going to suggest that you get a premade length of cable, otherwise you'll have to buy strippers and crimpers for this stuff, and a bulk roll of cable.
Here's a link to order a premade length (pdf file)
http://www.hyperlinktech.com/web/pdf..._worksheet.pdf
Here's a link to the different types of cable that you can use
http://www.hyperlinktech.com/web/cable_bulk.php
It looks like the coax cable you use for cable tv. This is much higher grade stuff. Don't try using cable tv coax. I've tried it, and it doesn't work.
I'll have to do a little bit more looking to find a router or bridge that has removable antennas.