However further research on this forum and others shows that this is insufficient for the Australian Immigration department and they seem to always request further evidence, apparently in the form of an affadafit from the biological father.
The biological father has has minimal contact with the child (about 4 visits in 6 years, abandoned the mother on hearing of the pregnancy and has paid nothing in child support. I made contact through his family to gain an affadafit but he avoided replying to any of my contact and seemingly is unwilling to sign the affadafit.
What other options are available to me now? Is there any other way of proving sole custody without having to go through a court? Does anyone have experience of gaining a visa for an illegitimate child to Australia that can advise me?