This is not meant to be legal or medical advice, per TOS.
I don't know, call me overly cautious, but I would hate to think that this could somehow jeopordize your workman's comp. Stranger things have happend. If they start the process of calling employers for your application, and HR is wondering how you can travel to a job interview
, sit for same, etc. it may not be in your best interest.
Also, unfortunetely, back injuries have a mind of their own. Your expectation and what actually occurs may be 2 different things. If you go back to work mid December, and you still can't function well, you need to allow yourself time to heal properly. You do not want to set yourself up for a chronic pain situation. And you may or may not find that your current employer makes reasonable accommodations for your injury,
Now, I have not a clue what this new position may be. However, if it is more "back friendly" than your current position, it may be something that would benefit you. However, I would be up front about the fact you had a fall, you are recovering from said fall, and that you really have wanted a position with them for a long time. But again, as you know, floor nursing (if that's what this position is) is not easy when people do not have an issue with their back.
So be mindful and careful. And maybe this is a sign that you need to think about management positions, something away from bedside.
Whatever you decide, best of luck in your endevours and recovery.