Hello,
Yes, you can do that. Since AppleCare has expired, you can replace the drive yourself. Of course, I don't formally recommend it without having some experience, but it isn't a hard procedure. The hardest part is having a way to migrate your data, if you don't have a Time Machine or other backup.
That said, just be very careful, as some of the internal components can be fragile.
iFixit - MacBook Pro has some step-by-step guides to help you out. Make sure you select the correct one for your particular MacBook Pro model, and read all of the steps completely.
C