50Km?? That's just down the street...!
This is Australia you're talking about.
I think the sense of scale and distance is vastly different between Singapore and Australia. I drive 50Km just to go to the shops sometimes! Last weekend, I drove to Melbourne - just under 2000 Km.
Let me see:
There is the Currumbin Sanctuary a few Km south of Broadbeach, there are numerous National Parks in the Gold Coast hinterland, up through Beechmont, Canungra, Natural Arch - far too many to mention. Then there is the Scenic Rim/Border Ranges national Park.
And of course, if you really want to see a "good" sanctuary, Steve Irwin's "Australia Zoo" is about an hour's drive north of Brisbane - so about 2 hours or so from Broadbeach (maybe a little bit more depending on traffic). Australia Zoo is well worth a visit, apart from being associated with the Irwins - it is really well done.
I see you will only have 7 days here, but there is just SO much to see and do, you'll probably run out of time anyway.
Oh yes - the other thing you may want to bring with you is a polarising filter - the sun can be very bright, with a lot of glare, especially near the coast (eg Broadbeach).
Hope you have a great time