As a Hunter, I've had two instances of challenges from people wanting me to not use my pet. One was a Rogue, so I said I'd not use my pet if he'd not use his weapons. Told him I'd even remove my Axe in that case and we could go hand-to-hand... He passed.
The second was a Priest, who eventually agreed I could use my pet, but couldn't have it out at the start of the duel... I agreed, as long as he/she started with no buffs on. These terms were acceptable to both of us... Little did he/she realize that whistling for my pet is almost instant, and the pet aggros even before he finishes drawing...
In general, I say use anything you have (legally) at your disposal. I use it as a learning experience to beat you (your class) when it counts... I'm not sure I'd want to burn any major potions for a duel, but if you do, go for it. Asking any class to intentionally gimp themselves? nah...
Now, if you are doing fist-fights, it's a different story, and fun as hell to do... Pants only, no weapons, no spells, no potions, no buffs and no bandaging (natural HP regeneration only). Just a pure beat-down until someone wins. Amazing how long these fights last (and how much running around there is)...