You can do anything that isn't instanced while waiting in the DF queue. On other words, you can:
- craft
- gather
- FATEs
- side quests
- any part of the story quests that aren't instanced
- farm mob drops like leather, eggs etc.

You can not do:
- leves
- guildhests
- any story missions that make you enter an instanced battle

The long wait for DPS is frustrating, but at no point in the game are you forced to just twiddle your thumbs while you wait. You can also shout for a pre-made (aka a Party formed manually with others on your server) while in the DF queue. The DF queue will automatically cancel if you enter a party manually.