I crashed my Phantom 3 advanced and bent my gimbal.  I have ordered a whole new gimbal and camera module ($259).  Will I need to re-apply my firmware to the drone after I install the new cameral module?

It depends what firmware the camera has on it.
When you power everything up, the app will tell you if a camera update is required.
It probably will require it, just download the latest 1.9 update and do the update as you normally would and just the camera will update as long as you are already on the latest update.

OK.  That is what I was hoping the answer would be.  Thanks.