The worst is that curing a zombie takes very long (~5-8 min) and you'd better not go too far from him otherwise he would despawn... So while he is curing you can simply NOT really play... I typically leave the game alone and do something else! Please fix!
Sorry, my mistake... I'm using a MineZ texture pack! No carrots there! (but it's so close to the default one I forgot about it!)
=>close!
Same in 1.6