If I want to take my girlfriend to Australia, my family will let me study at Royal Melbourne College in Australia.

It's best to let your girlfriend apply for a school and then apply for a student visa.

Although the Australian government recognizes unmarried couples in theory, it is difficult to apply for your girlfriend's visa without a marriage certificate. When applying for a student visa, you should write your girlfriend's information on the form 157 as an unmarried partner.

Then you have to provide a lot of proof that you are indeed partners. Note that it is a partner, not a couple. Relationships between lovers cannot be regarded as partners. Your partner needs proof of cohabitation, including bills, photos, joint accounts, joint real estate, etc. It's in the same place, so it's very troublesome and difficult to handle at all.

If you have reached the legal age of marriage, I suggest you go to the Civil Affairs Bureau to get a marriage certificate, otherwise it will be difficult to accompany you to this visa.