I have several projects based on JQM so I’ll tell you what your options are…
If you have too much time invested or you’re too near launch to pull back now you still have some options with JQM.
The Good News:
JQM was updated to 1.5 and moved from Alpha to Beta status and the 1.5 does use the later versions of JQuery.
The Bad News:
1.5 is not a drop in fix. All of the things that were deprecated and planned for removal in 1.5 were, indeed, removed. This means that a lot of your page handling code will need to be rewritten and you can expect things like your headers and other controls to need work.
The Jquery team seems to be in disarray. The guy who was working on JQM has left the project and a lot of the JQM controls have been moved to JQUI or dropped from JQM because later versions of those controls already exist in JQUI. Their thinking seems to be JQM will die and you will use the Jquery + Jquery-UI + plus some page handler + some swipe handler. The result will be big, fat and slow AND as is typical with JQuery, they’re sticking with a web based strategy while the world is moving to mobile access. In the forums, their own moderators are telling people to NOT start any new projects with JQM.
If you need to use 1.5 just to get this version shipped, it’s probably your best and fastest bet BUT you will eventually have to rewrite.
I have found Framework7 to be the easiest port. It’s free, pretty easy to understand but (fair warning) their developers can be very snarky in the forums (but so can JQM’s). You can find Framework7 here.