I actually have experience with working in this manner, so yes it is possible.
The best way I've found to do is for each of you to get a free Dropbox account, then share a folder with each other and have the quest file save to the dropbox directory. Quest has a little known feature that will detect when a file you're working on has been modified (while you have it open) and will prompt you to reload your open copy with the latest changes.
You do still have to do some coordinating though, to make sure you and your partner don't start working on the same thing at the same time, because your changes will keep overwriting each other. But this is the best way I've found to do this so far.
That being said, it should also be possible to use some kind of source-control service like SVN, Git, Mercurial, etc. to be able to make pulls and push changes. Or even using some sort of web-based collaboration software like FengOffice, where you can check out the file, make some edits, then check it back in afterwards. These solutions mean only one person can work on the file at a time, but it removes the problem of overwriting that I mentioned above.