Click the name of your realm and you'll get a popup that asks you if you want to install it. Accept and you'll get the crummy icon I made in your list of search plugins. Then just type the name of the character you want to look up on that realm for and Firefox will take you straight to the Armory page for that character. The catch with this search plugin is that if you don't type the exact name of the character you're searching for, you get an error page at the Armory. That's because in this case we're not really searching, we're just trying to go directly to the character sheet.
World of Warcraft is a trademark of Blizzard and I'm not affiliated with it in any way, just another player.