Today I played a game with Poppy in which I got utterly fed (I ended 19/3/11) but failed to carry my team since no one pushed any line, and I was unable to splitpush because Poppy's too slow killing the minions. The Items I got were Iceborn Gauntlet, Dead Man's Plate and Zz'Rot (gotta push!) but I still couldn't do anything (later I got Mawmalwtiuosiajsks and Titanic Hydra but I still couldn't do much).
Is the any Poppy build that gives her good splitpushing while conserving her "champion fighting" potential? Any suggestions are welcome (if nothing works then I'll go and carry with Diana/Fiora who have no problems pushing).