Yes, the process you mentioed is fine:
1. backup site contents (SQL, html and php files)
2. Point domain to the new host
3. Once you receive login info from the new host, re install directory script, upload SQL and PHP/HTML files.
4. You may need to change path to some files.
Test site to ensure its works perfecly.
5. Give yourself a pat on the back and have a cup of tea
