Nice, but this is better (and you should try do even better than it :) ) Rated 3 out of 5 stars

I have to say that based on the description and comments there is already almost exactly similar extension except there are no problems with link id's cluttering the way - it works by showing id's only when requested (by activation key). If it ever messes up by using same hotkey as FF or another extension you can change the keys (or use keyconfig to change the other key).
It's named LoL and it's a fork of an old no-longer supported HaH (Hit-a-Hint). It works perfectly with any links, dialogs, fields, etc... Press Ctrl while writing the hint number and you can open the link on new tab even!

Still do note that I'm not here to offend - I wish the best for your project but for now IMHO the one I use is the best choice. I might start my own for of it however as it does not offer one feature that I would really love to do without mouse: Copy a link or image address!
Still, maybe if you can reach the minimum of same quality that LoL has you have good chances - and if on top of it you do what I said to miss in LoL too then you will most certainly have me switching from LoL to Mouseless Browsing. Provided that you achieve that before I make my own for to do it that is ;)

This review is for a previous version of the add-on (