As prot, you will have the advantage verses other melee classes (rogue and warrior in particular, but also pallies and in a way, hunters), but won't usually have the massive amount of damage to take down clothies.
If you were to switch to fury or arms for pvp (arms is better) you will get massive crits and burst damage, meaning you can take out clothies in a few hits if you have enough rage. However if you were to come up against a prot warrior, you would have a hard time because of the amount of damage reduction they have.
Unfortunately that means that while you will win a lot of 1v1 fights as prot, it can take a while before you do win. In bgs by that time usually they have brought support, or have run away, so you will have a problem there.
As for leveling as prot you sure can, I did it from 60-69. It is slower though, and I spent a lot of time in instances rather than just pure leveling.
I would suggest getting a hold of tbc though, as the gear and content of outlands is amazing compared to pre-tbc. However if you want to pvp a bit, stay at 59 as you will dominate everyone else in AB and WSG, or you could ding 60 and proceed to tear it up in AV, and you will of course have the lvl 60 pvp gear you could buy as well.