To get a minifig from one project to another, you will need to use the import tool under File > Import...

One thing that may help is to isolate your minifigure. Open the model that has it and then use File > Save as... and save it as the name of your minifig. Now you can safely delete everything except your minifig and then of course hit File > Save to lock in the changes. Now you can open your other project and import just the minifig. This will work for any file that has parts you want to move around.

Hope it helps!