Firstly, travel insurance. I'm the WRONG person to ask at the moment as I'm still (yes Paula STILL) battling through a hospital claim from last year. Right now I'd say it's all a big waste of time but you should seek advise from others. The more I travel the more pointless I think travel insurance is. But that's me.
As for your accommodation, again, it all depends on what kind of traveller you are. If you're fairly new to all this hobo malarkey it can be a little daunting and so the natural response is to try and plan it all before you go, cos' it feels nice and safe right? And you CAN do that. Check out something like www.hostelword.com and book away till your heart's content. There are hundreds of cheap, reliable, clean and very appealing accommodation options out there. You don't even have to stay in a dorm, you can have a room all to yourself if you want. Seriously, you could have all this (Singers, Cairns, NZ) booked up inside of ten minutes if you want to. BUT, do you really want to? What about the adventurous streak in you? What about the excitement of not
knowing? Booking everything now will mean security yes, but then that's it, there's not a fat lot else to do then. What if you meet some really interesting people on the plane or train or bus? People who tell you about the perfect place to stay that's full of exciteable like minded travellers like you and they're headed off tomorrow to some other place you hadn't even planned for? "Wanna come Dan? It'll be a hoot!" I'm saying this cos' this is exactly what happens. And what I'm getting at is there is so much to get out of going with the flow and being adventurous, yet so many people don't do it, so many stick to 'playing it safe'. Plus, travelling Singapore and Australia is an absolutely doddle. It's made to be easy, which is why you won't have any problems.
Why not read few a few blogs and see what other people's first -hand experiences have been? Failing all that and like I said before, you can crash at my place for 70quid a night and I'll throw in a killer feed and a few coldies to keep you going..