someone landed on my blog the other day after running that particular google search. unfortunately, while this is a reasonable question to ask but there isn't much here to answer it, so our intrepid googler left empty-handed. time to fix that.
why is it a reasonable question to ask? well, when you look at the turnip's spells they're almost all elemental, which makes it strong against mechanicals (rarely encountered in the wild) and weak against critters (which are everywhere in the wild). meanwhile, aquatics (which are fairly common) are strong against it. so, fighting with the turnip is like fighting with one hand tied behind your back. in addition, most of its spells include some form of self-healing (such as leech seed) or damage mitigation (such as sons of the root), and therefore do less damage than purely offensive spells. there's nothing wrong with this, except they lead to longer fights, which means fewer victories (and less experience) per hour.
so what do you do, given the turnip's limitations? the answer is, don't
use it. put it on a team with at least one level 25 rare that hits hard.
my personal favorite for this is francois the darkmoon monkey, but
there's lots of other good pets for this job. a second level 25 that is strong against pets that the first one is weak against is ideal, if you can do that. then, go pick fights with wild pets that are much higher level than your turnip. after one round, swap the turnip out and send in your level 25, and unleash hell. the fight will be over quickly, and the turnip still gets half of the xp it would have gotten had it stayed in and managed to win the battle entirely on its own. after the fight, the victory heal will get the turnip back to full health, and hopefully the level 25 pet somewhat close to it. then you can quickly move on to the next fight.
this method becomes a lot less effective when you reach level 20 or so, and try using it against cataclysm or pandaria pets, but this isn't a big deal. the value of the turnip is when trying to capture low-level pets, the ones that can be one- or two-shots by conventional pets. against, say, level 24 pets in the valley of the four winds, the danger of accidently killing a pet you want to capture is pretty minimal, so it isn't necessary to get your turnip all the way to level 25. i've set mine aside now that he's reached 20, to be saved for the day i happen to encounter a, say, silithid hatchling.
so, that's how i leveled my terrible turnip.