The very first thing you should do is point any kind of profiling tool towards your software. If you can't do that (like, if you haven't got such a tool), insert logging code.
The very first thing you need to do is figure out what is taking a long time to complete, and then why is it taking a long time to complete. That your "copy" operation as a whole takes a long time to complete isn't good enough, you need to pinpoint the reason for this down to a method or a set of methods.
Until you do that, all the other things you can do to your code will likely be guesswork. My experience has taught me that when it comes to performance, 9 out of 10 reasons for things running slow comes as surprises to the guy(s) that wrote the code.
So measure first, then change.
For instance, you might discover that you're in fact reporting progress of copying the file on a byte-per-byte basis, to a GUI, using a synchronous call to the UI, in which case it wouldn't matter how fast the actual copying can run, you'll still be bound by message handling speed.
But that's just conjecture until you know, so measure first, then change.