Help needed changing domains.

I’ve got a functional premium press directory that I need to change to a different domain name.
Both domains are on a shared server using cPanel for management. I tried backing up the wordpress installation using Duplicator and re-installing it on my local host without success. All I got was a site without images.

This makes me a little wary when it comes to trying it on a live install. Temporarily, I’ve got the new domain aliased to the old one but the old domain expires in a week. I really don’t have the time to create a fresh site if it doesn’t come off.

Any help will be appreciated.