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

Yes. 

If you have a Personal license, and you want to transfer the license from 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.