Moving to a PS4 Pro

I'm sure this has been asked a lot, but doing a search on it only seems to bring up a lot of answers which don't seem to actually apply to this particular question, or "that (maybe) should work".

I am going to be getting a Pro, but I will be using my original 2013 PS4 as a trade in, so I will not have both systems at the same time. Will this course of action get all of my stuff (including P.T.) transferred over to my Pro?:

1. Use an external HDD and the "Backup System" option in System Settings on the old 2013 PS4 to backup the entire system.
2. Remove stock HDD on Pro and replace it with a new 2TB one.
3. Initialize the new HDD on the Pro, and install firmware via USB thumb drive.
4. Hook external with old backup on it to the Pro, and use "Restore System" option in System Settings on new Pro.

Am I missing anything?

Thanks.