Change wordpress host

I need to change the hosting on my Wordpress site.
I have a new, unfinished site and could do this myself but I'm no expert so prefer to pay someone.
The site is currently an addon domain at my host and I want it to be the primary domain so it needs moving within the same hosting set up.
Set up a new WP (1 click!), download the old database, export the content, ftp the files and I think that's the bulk of it.
A quick job so low offers please!