Oh man. I am so sorry that it has come to this for you. I am sure though that you are resolute in your decision under these circumstances.

Is there a reason you a flying to Sydney? You can get a bond loan or a DOH house in QLD because you live there, but coming down here will mean you can't go on the list straight away or get the loan until x time as a state resident.

Else bond is 4 weeks of the rent amount - plus you need 2 weeks rent in advance, so 6 times whatever price rent you are looking at.

If you can both come to an amicable arrangement on the kids thats great, but as BG says, get it done legally so that if things turn sour you have that supporting you.