She's short and ugly, that's why nobody plays her. Same reason nobody played much Gragas or Urgot - then they got some tournament play, and bam, suddenly super omg OP. She's sleeper.

1260 + tabi (+ philo) isn't that much gold, and her farming isn't bad, it's just her lack of AoE.

No, I highly doubt she's sleeper OP. Her lane phase is incredibly weak. She's too easily harassed, and if she tries to harass back, then she will use up a lot of mana. If it weren't for her passive, she would be very underpowered. Also, Poppy was played in one game in the Season 1 World Championship, and she did terrible. Granted, that was a long time ago and things have changed, but she still is somewhat UP because of her incredibly weak early game. However, in S3 she may become more viable with all the items for melee champions.

Poppy has a really hard time farming early on.

She has very limited range, and no sustain.

She's far from OP...

Psst try playing poppy urself. She's only 450IP

Did this Poppy catch you stealing her red after she placed a ward, then she slammed you into the wall of Red and killed you, to which you said "WOW"?

yeah... but... she is easy to counter

Having no early game makes no sense. Poppy's ult is one of those abilities that makes her instantly better once a point is put into it. Versus someone like Teemo who gets 1 mushroom as soon as he puts a point into it. To me her late game isn't very strong since her ult doesnt add much as you level it up. Versus yet again someone like teemo who, after going on for 15 minutes after he's been lvl6 has been building up his shrooms across the map.

Just because her ult is instantly useful, vs say a Teemo who only gets 1 mushroom at lvl 6, doesn't make her OP.

when she ults someone else, you can't damage her. so technically you were right, she was impossible to kill (for 6 seconds).

try fighting her when she hasn't ulted someone else. and you're welcome.

She has no early game because she is easily harassed, and due to her lack of range it's hard for her to harass back. Sure she has a charge and her Q, but that takes up a lot of mana. Constant harass makes it difficult for her to farm. When she reaches level 6, she gets her ult, but it doesn't make her instantly better. In order for her to make good use of it, she needs damage so she can kill someone, but she won't have a lot of damage at level 6 because she won't have many items.
At level 18, when she has a lot of items, she will have a lot of damage, so she can ult someone and pretty much instakill them because her damage is so high late game.