Start UVHM asap unless there's a must have piece of gear you really need as you can only get up to lv50 gear in tvhm and in uvhm gear gets crappy really quickly once it's under the level of the mobs, and as you're already level 51 you'll be starting uvhm with lv50 gear against lv51 mobs, raise your level any higher and the level difference will only increase. It shouldn't be too bad not having the best gear as there's some enemies early on that can be farmed for decent legendaries anyway (knuckledragger - hornet, bewm bewm - bonus package, etc). One thing to make sure though is definitely make sure to have a slag weapon. Slag is even more effective in uvhm and is arguably the most important thing to use