Are you sure the problem is with the transmitter? Or did you lose the plane, camera, transmitter and all?
To answer your question, yes. You can buy FatShark or other brands of transmitters that will work with your Teleporter goggles. There is no "binding", but you have to be sure that whatever transmitter you get will operate on one of the channels supported by your goggles. Check your documentation to see what frequencies are assigned to the various channels. The easiest solution would be to stick to the FatShark brand of transmitter. I know that Foxtech FPV carries a 32 channel transmitter that probably supports the frequencies used by your goggles.
As for the camera, it too doesn't have to be a FatShark camera. Be sure it operates on 5v so that it can be powered by your FatShark transmitter (should you go that route). But you could also use an 808 #16, Mobius, GoPro, Sony board cam, and others. There are lots of reviews on cameras.