Would like to offer my perspective.

I would not be looking purely at brand recognition of potential employers but also alternative exit strategies. Many people don't actually end up in jobs for which they studied for at university. I would advise thinking about entry requirements for programmes like MBAs, JDs or post grad MBBS (or whatever it is called. I would also advise considering whether a mid-way transfer between programmes is an option in the event you realize half-way through that business is not as interesting as you thought it would be.

Ultimately, private degrees in Singapore would not afford you the same postgrad opportunities as a degree from uni of Melbourne. My suggestion would be not to limit your exit options at this stage - go to uni melb.