I myself is coming from the private degree like your despised RMIT degree.
If you are asking me of how am I doing with my peers from local unis, I can say that I am doing very well and maybe well ahead of them.
Just for info: my degree is for SWE and i m working at bank
And if you are asking me of how important a degree is, I know of someone that did not have degree, but he is a SWE lead in a bank. However he have 25 years of exp in SWE. He only started taking part time degree recently. Nevertheless
IMHO its all based on your actual skillset and some luck/faith and confidence in yourself!