What's my chances of getting a rental?

26, single with a child, good rental history but I'm only bringing in about $700 a week from work and $800 a fortnight from centrelink. With how everything is i feel like i don't stand a chance. Would want to be anywhere between the city & Sellicks.

I know i should get a better paying job for success but I've been working 2 jobs, 1 full time and 1 casual since my son was 4 days old and I'm so burnt out so I recently swapped my full time for part time.