DIVORCE

These are hard issues and many parties and lives. I would not relay on any forum or internet with issues dealing with a child and foreign laws. I recommend a lawyer in AU to help with these issues.
One wrong step could make it worse.
Wish you the best.

I agreed with Taxasbrazil but the only difference I would recommend you get a Brazilian Lawyer. I haven't found to many foreign lawyer that know Brazil laws. Usually the lawyer will have to meet face to face with the judge in Brazil in the city you were married. If you get this resolved please post the outcome.

Dear Emilybds,

I did not understand this part of your message: "If I go to Brazil can the father force a paternity test? And cause problems for the child to leave the country even though he is not on the child's birth certificate?".
If the father is not on the birth certificate, the divorce procedure is different.
But I understand that the father may be able an injunction to prove his fatherhood and yes, create complications for the child to get out of the country, yes, as difficult as that could be,  though. 
In most cases, divorces will be able to be resolved without your presence here, with the use of a Brazilian lawyer.
Best,
Sergio

I don´t see any benefit of mentioning the child at your divorce in Brazil unless you´re asking for a child support. That would definitely complicate the matter as the courts and the father could seek an injunction especially if he was born in Brazil. That could create complications for you and the child with all the stress, bureaucratic delays, expenses and time lost during the process. Could you file that divorce in Australia? His absence alone without the moral and financial support should be grounds for said divorce. There´s got to be provisions of the law in Australia allowing such measures. You should consult a lawyer there. And you should avoid bringing the child to Brazil and should come alone to file for divorce if you decide to do it here. Then go back to Australia
ASAP and let your attorney handle the case. That would cost you about R$1500 (reais).

If he was born in Brazil, he is a Brazilian citizen by virtue of Jus soli. By Jus sanguinis, you need a DNA test to prove he was fathered by a Brazilian to be a Brazilian citizen...

robal