What you are suggesting is already implemented in the search box.
afaik the search feature only searches the content of the posts. not their username. so if you search for your username in this thread right now you'll only get my post as a result because your name is written in the quote.
if it is there and I missed it please tell me. it will help a lot.
True, only quoted posts are included in the search. Although another thing you can do (if the thread is small) is click on "All" after the page option and just Ctrl+F the username