Have a look at this tutorial here: HOW TO - Upgrade your iOS Jailbreak
Yes, it talks about upgrading/restoring with iOS 4.x, so it's an older post - but the steps are the same ... except for step 3.
When you get to step 3 in the tutorial, use this instead:
3. Put your device into DFU Mode (DFU Mode for Dummies) and restore the iOS version you are moving to using iTunes (in your case, to iOS 6.1.2).
Then follow this tutorial to jail break the iPad using the evasi0n 1.4 tool: TUTORIAL - Jailbreak the iPad with IOS 6.0 to 6.1 using evasi0n
Once you have finished you should have a clean iPad freshly jailbroken with Cydia on it!
Once your iPad is jail broken, you can then move on to step 4 in the tutorial.
Hopefully, this will help. Holler back if you need more assistance. Regardless, do let us know how you get on. Good luck.