Hi Carlos,
From looking at your domain name it is still pointing to Melbourne IT's servers for the A record (when you use it to go to www) but there is no MX records which what you use for mail routing.
What i think has happened is you moved your email to 365 and pointed your A record to the 365 servers. But as far as transferring your domain name registration i think that is still with Melbourne it. Also i don't think you can move the domain ownership to Microsoft. This you have to do with a domain company like 1&1 and go daddy.
I would go back and speak to MelbourneIT and see if they can do anything.
All the best.
JP