There are quite alot of better junglers out there, but Poppy is viable. I tend to only do it in games that don't matter, like AI, but certainly don't go doing it in ranked - you'll look like a troll and you may throw the game, if for no more reason then causing conflict in your team with an irregular pick.
When I jungle Poppy, I start W, which gives her mobility and alot of extra AD and armor which helps her early jungle. Next I'll take Q to clear camps faster, and finally E for some CC while ganking(if you can land it against a wall). I'll usually max W first.
Be warned, though, Poppy uses quite alot of mana in the jungle, so if you can, you'll want to steal blue(which is why I like to use her in AI games). Otherwise, it will help if you have a manaless mid like Kat, Vlad, or Akali, so you don't have to donate blue.
Your build should probably be similar to what you build for top, with maybe the addition of a wriggle's early.
Edit: I also like to take mobility boots in the jungle, which I don't do in top lane, but that's a personal preference and if you don't normally jungle mobility boots, you may find that Poppy's speed boost from W is more then enough to get you around.