Hiya
I have an Aussie bloke too. But he didn't work for the
International Schools, except for an Art & Design School in Singapore. He has worked in the British Council as well.
Your salary back home would be about $6,5K a month eh? My guy's was never that high, esp when he's an English Teacher but I'm sure the International High Schools and stuff pay their expat teachers fairly well, with medical coverage. I could ask around for you and get back to you with an estimated figure. The local equivalent of the superannuation here would be the Central Provident Fund. That's just for us locals and doesn't apply to the expats unless you're a Permanent Resident.
An apartment in town would be about S$1,800 for a 2 bedroom and the price goes up depending on the size, location, facilities, if it's near the train station it's usually more. But if you're sharing it with someone, it can become affordable. A room with an ensuite bathroom could be about S$600 to $900 depending on the weekly maid that comes over to clean etc. Otherwise, big, breezy, walk-up apartments albeit old, are a another great option. But if you're into the facilities (pool, gym, tennis court etc), the prices of those apartments will go up. (I used to do real estate, for expats). And I'm kinda fond of walk-ups because they're just awesome! It all boils down to whether you're keen on lots of green and space in your environment or not. Coming from Australia, I know it's important for you.
Anyway, I could ramble on but I don't want to bore ya. Hope your decision making does well.
Cheers
Immortal