Can I make this transfer?
 

arrive from Mel 05:20.
depart on UA 07:20.

If I can't make it, what can I do in the airport for 9 hours?

you should have no problem making that connection in SIN. If you prefer to spend the day there, there are many options to fill your time. go to singapore airlines site to get more info. another note, if possible i would try to fly singapore air if at all possible. they are in a whole different class than our pitiful us flag carriers. have a good trip!