I understand you would like to change your DNS hosting provider from Melbourne IT to Go Daddy.
From Office 365 side, to make sure you can work with Exchange online service normally, the required DNS records should be created correctly. For example, before you move the domain from Melbourne IT to Go Daddy, the required DNS records should be created correctly at Go Daddy. However, DNS records always need to take a period of time to take propagate through the DNS system. For will it affect the Exchange online service during this period, it is recommended that you contact your domain hosting providers to get a better responses. Thanks for your understanding.
Regards,
Maggie Li