Having recently replaced the drive on my PS4, backing up to an external HDD really made getting everything back on the new drive much easier and faster than downloading everything again. Keep in mind a couple things though: First, it takes a pretty long time to copy 300GB of data (twice, actually, since you are going to copy it back to the new drive) and second, some people mistakenly think you can play games directly from the external backup drive. You can't.
Good luck on your HDD replacement. It's straightforward and you'll enjoy your PS4 much more when you aren't constantly searching for things to uninstall to make room for new games.