And by early I mean at like level 2 or 3 and probably with just half complete jungle item.
With how strong Drakes are, I think it's wise to practice jungle for the sake of early Dragon taking.
Edit: So i tried out 
on a blind pick, he can take dragon quite easily but you'll have to know where the enemy jungler is. Managed to get 4 dragons though (with ocean soul), unfortunately didn't get the chance to kill elder dragon.
Also remember, dragons are a little squishier this preseason.
So, Warwick.
If you put 2 points into W, you can take any drake at level 3 effortlessly
Wick, fiddle, probably AS Shyv and Xin if they dressed with that in mind...
Maybe nocturne depending on if the enemy doesn't come after him.
I've taken Dragon at level 3 on Shyvana with 
full health, Smite and 2 refillables. I don't recommend it though. By the time you're done you will have like 10 HP. You risk feeding.
Shyv and Yi can do it at level 4.
I think Udyr, Olaf and Shyvana can as well.
I hope Nunu can as well but I haven't seen him around much lately.
WW Olaf Shyvanna Heimerdinger VI
Taric can do it right at 5 minutes with 
without losing hp. Taric can also win duels at that point while taking dragon against most other junglers if he can switch dragon aggro over to them.
Pardon the sound. My comp just updated and my headset didn't work for some reason so it was picking up noise through the laptop microphone. https://www.youtube.com/watch?v=LHJMFN0HT1I
Nunu can do it.
Level 4 champs that can: 
I know these can early not sure the level: 
Vi, Nidalee, Lee Sin, Elise, Nunu, Shyvana, Udyr, Warwick, and Olaf are the only ones I can think of off the top of my head. I haven’t tried out Kha’Zix, but I’m fairly certain with his isolation passive and built-in sustain he should be able to now that dragons are squishier.
i played with a silver Mundo jungle once, and he took dragon at lvl 4.. my buddy and i were duoed, and at the same time we both said "fucking mundo??"
