That might work if the version weren't almost three years old. You will simply install problems and headaches unless you take the time to upgrade.

Do the backup of your old database, install 1.3.8a on the new machine, remove the 1.3.8a database and replace it with your old 1.2.5 database.

Go into install again and perform JUST a Database Upgrade. Once done, your old database will be updated to 1.3.8a and you can continue on with setting up your store.

Be sure and read the override tutorials when starting out. Go to https://tutorials.zen-cart.com and search on overrides. There are at least three good articles.