I play a tank and quite often spend less than a minute in queue before getting a party. If you are DPS, get a tank or healer to party up with before joining the duty finder, otherwise just deal with the long waits. Or play a tank or healer

And yes, the servers are full. Have you been to Quarrymill? So many people the game can't even render all the characters, and that's with max settings. One reason the servers are so full is that people aren't logging off because they don't want to have to try for hours on end to get back in. I liked how in FFXI there was a setting for how long to wait before auto logging off. I always set mine to never to do it, but I think the default was 15 minutes or something. They need to bring that feature back for this game.