I can get your site and associated database transferred to your new host, test it, then switch DNS.
Transferring the name itself needs to be done on your end and the procedure varies.
Relevant Skills and Experience
I run a web hosting service, work here full time and have extensive site migration experience.
Proposed Milestones
$5 USD - New employer to Freelancer - Full account setup milestone.
$25 USD - Site copied, tested and DNS switched.
Additional Services Offered
$15 USD - Help with domain name transfer, if this is really the case. (Just switching DNS to point to the new host is covered in bid, which a domain name transfer is a whole other thing and should be done after the site s transferred.)
I charge per platform, so if you have others mixed in with your Joomla, it will affect the bid.
PS: I see you only selected "Joomla" for the category, while this also falls into "web hosting" and "website management", which I have plenty of completed jobs under (see my profile, right side).