Thanks to all for taking the time to respond to my question.
I'm reluctant to go down the DNA path, because it's (in my view at least, and for various reasons) unlikely that her "stepfather" was her biological father. Thus I'd be paying a fair bit of money to probably prove the negative, even if I could identify his relatives and convince them to collaborate with me from 13 000 miles away.
In relation to my grandmother's marriage certificate, that's an interesting issue. She travelled to Australia by ship alone aged 16-17. She married my grandfather who was about 13 years older about 5 years later. In the circumstances, it was unsurprising that she had a false name for her father and a false (older) age on her marriage certificate. That made even tracking her down difficult.
Again, many thanks to you all.