Theirs absolutely nothing wrong with my suggestion, it worked for me. When you buy your drywall just make sure your not purchasing a thicker piece then the wall. 3/8" should be safe. I have patched a hole similar in size myself using that method and its been there for over two years now and no problems since. Remember the mud is mainly on the drywall. Only a thin layer spreads over the plaster so I have never had a problem with this method yet. Also the drywall is secured into the stud as well. Like said I have not had a problem since. Good luck.