Yes, indeed.  A business name, company name or a domain name does not of itself give you any rights to that name.  Whereas an Australian registered trademark gives you the right to use and stop other people using your name in respect of your registered goods and or services in Australia.

In Australia, TM denotes that you have either a pending Australian Trademark application or a common law trademark in Australia, whereas the R denotes that you have a Registered Trademark under the Australian Trademark Act.

In Australia it is best to apply for your trademark in ordinary typed letters as this provides the broadest protection.  That is once registered, you have protection for any stylised rendition.

In Australia it is generally best to apply for your logo mark in black and white/greyscale as upon registration, you have protection for all colours, unless colour is of particular significance.

This information is general in nature, please contact me for advice regarding your particular situation.