Assuming the machine-name will change, then make sure you run sp_dropserver/sp_addserver (Step L in the linked article). Definitely a gotcha step.

I've never migrated an existing database server between domains; I have renamed a server, and that causes sufficient hassles!

You don't mention if your current server is virtualised or physical?

Depending on the complexity of your current server config, I would be tempted to start with a fresh install. Again, depending on your IT infrastructure, a new OS might be a few clicks in HyperV/vSphere. Followed by MSSQL install and data migration. If you have a physical machine, then not to easy to accomplish.

Andy