Can I Transfer the Elementor Pro License Key From One Domain to Another?

Yes. 

If you want to transfer the license to one domain to another, please deactivate the license from your former website in "Elementor > License" on your WordPress Dashboard, then activate the license on the new website. 

You can check where your license is active in your account on https://my.elementor.com/  via  View Websites > Manage License.