What can be caught?
Legally - nothing (except possibly a corella)
What you might see is sleepys, inland beardeds, sand goannas, MD. Possibly even a Fierce snake but you may be a touch south for them.
You can follow the Darling river south from bourke along a dirt road (its lonely out there, be careful) for about 400 km. Saw a lot on inland beardeds there