Pangu was released a couple days ago to handle jailbreak for ios7.1-7.1.1 devices. The jailbreak seems to be working alright.

Personally, I suggest just staying on 7.0-7.0.6 for now as the 7.1.1 update is not really worth it for the effort. However, if you think you need to get to 7.1.1 you should do so soon. Apple is expected to release 7.1.2 any day which will close the signing of restores of 7.1.1.

For those having issues in a boot loop after the jailbreak you might try shining a light at the light sensor. (http://www.reddit.com/r/jailbreak/comments/294wob/jailbreak_with_pangu_and_bootloop_try_this_fix_oo).