VBAC'ing at any hospital really comes down to your care provider, especially in the public system, as you can't choose who to have at the birth. However, if you can educate yourself, possibly hire a doula and find women who have VBAC and who fully trust in women's body to birth their babies, when they are left to do it.
Queanbeyan hospital is very supportive of VBAC and is predominately midwife led care, it really is a beautiful hospital to birth at, ACT residents can also birth there.
I would also consider hiring a Doula. They really are a wealth of knowledge and can help you with navigating the hospital system to support you in achieving your VBAC. They are also a familiar face in the labour ward, which is very reassuring for you and your partner. They will support your emotional and mental health and if the birth results in a c-section they can help you feel empowered & in control. I may however be just a little bias as I am one. However, the stats speak for themselves really.
Where ever you chose to birth, I wish you all the very best. I am happy for you to PM me if you have any specific questions.
Yours in birth