Kathy, I'd recommend keeping UFT on both your machines if they will support it. One obviously remains your primary one, but after doing a backup, load it onto the secondary machine to ensure it works (e.g. no bad disks or failed backup step). Now you have three backups: your main computer, the secondary, and the disks. And keep several generations of backup disks around to be a bit safer (maybe give them to relatives to store out of your house).
As you seem to be just starting, you probably don't have much on your database, but if you work at it for a while, you will have enough that you don't want to have to re-enter it all if something goes wrong.