You can take a pet from lvl 1 to 25 in under 10 minutes if things go in your favor (19 fights if you have the hat).
You'll need two 25s (well, don't NEED, but it helps), as well as a friend or second account that also has two 25s.
Both players then pick a 3rd pet of matching lvl, and then simultaneously queue for a pvp pet battle. As soon as the battle begins, one person forfeits (you don't even need to pick a pet), giving the other one 1000+ exp for most lvls, and slightly less once you close in on 25.
You'll occasionally run into others queued for pvp at higher ranges, but it's not terribly common and will only add a minute or two to 25 at the most. Just quit the fight, and re-queue.
Edited, Jan 17th 2013 7:13am by Reiterpallasch