Ms Romulo has battled for years in a failed bid for permanent residency and faced being separated from eight-year-old Giro, who cannot leave due to partial custody orders with his Australian father.
Ms Romulo and her two overseas-born daughters, aged 12 and 13 from a previous relationship, were issued a final deportation notice two weeks ago by the Home Affairs department for July 11.
A previous application for ministerial intervention was rejected by Mr Hawke in December but she secured a number of short bridging visa extensions amid media coverage.
Ms Romulo said she was relieved and grateful for the outcome.
"The feeling of leaving Australia is gone," she told reporters in Brisbane.
"I’m so thankful to our assistant minister, to give us a chance to stay together as a family.
"They’re (the children are ) laughing from here from side to side, the little one is so happy."
Ms Romulo's lawyer Angus Francis is urging the minister to consider granting her a permanent visa.
"The case will be reviewed in 12 months time by the department and the minister and we’re hoping before then, or then the minister will grant a permanent visa," he said.
"They haven’t given us any indication at this point."
Mr Hawke's office previously said the minister and the department had comprehensively assessed Ms Romulo’s application and ministerial intervention only happens in a "relatively small number of cases which present unique and exceptional circumstances".
Ms Romulo came to Australia as a dependent on the 457 visa of her former husband, and father of her two daughters, almost 12 years ago and has not lived in the Philippines for 18 years.
The aged-care worker entered a relationship with Giro’s father and when they separated became her Australian-citizen son’s primary carer.
“Child custody matters are beyond the scope of this Department and are addressed through the appropriate jurisdiction of family law,” Home Affairs previously said in a statement related to the case.
Under the Migration Act, either Home Affairs minister Peter Dutton or his assistant minister can intervene at any time.
Section 4.2.8 of the legislation’s guidelines provides for intervention.