jiejie

If you haven't been to Melaka before, head there. There are express buses leaving in the morning, google a bit and see if you can pick up something directly from SIN, or have to head into the central city first. You can also fly SIN-KUL and head south from KLIA (google for how to do this). If you've been to Melaka already, head for KUL. Easier to get to/from city from airport than CGK, and less immigration time and hassle. You want to leave yourself options to get back in case of weather or IRROPs. With Kuala Lumpur, there's always road options. CGK, you're screwed. CGK is not worth going that far just for a daytrip.

And yes, you'll need to go through SIN immigration, which is pretty painless. If your checked luggage is already through-tagged to Australia, you can ignore baggage claim. You shouldn't have any visa issues entering Malaysia, just keep your passport handy.

Edit to add: I forgot, but I thought Melaka has recently upgraded its airport, so if interested, flying directly there from SIN or Johor Bahru might be possible -- I don't know who is flying into there.