I know some top web hosting companies in Australia (Hosting Australia, Netregistry, Crazy Domains, VentraIP Australia, Zuver, Net Origin, UberGlobal, Relentless Hosting etc. ) and I've experienced in working with some of these companies.
I'm expert in WHMCS and cPanel/WHM so I can assure you that migration will be performed perfectly with no issues at all.
Please let me know if you have any queries or concerns.
Thanks Ameya Barwe.