It's just as well you were declined for the 'Woolworths Everyday Money' card as this does *not* earn Frequent Flyer points, it earns everyday reward points. You would have had to apply for the Woolworths Qantas Credit Card, which earns at 1 point per dollar.
I suggest you start by looking at some of the Frequent Flyer Program pages on how to earn points from sources other than flying.
Qantas (Qantas Frequent Flyer):
Frequent Flyer - Earning Points
Virgin Australia (Velocity Rewards):
Earn Velocity Points | Velocity Frequent Flyer
American Airlines (AAdvantage):
Earn Miles | Award Travel And Bonus Miles | AAdvantage | AA.com
Emirates (Skywards):
Skywards: Earning Miles | Skywards | Emirates Australia
If you're basing yourself in Australia and flying domestically, i'd rule out Emirates as it's just not an effective program for domestic travellers.
Other programs are mainly international, but if you go to the homepages of the airlines, and look at the Frequent Flyer programs they have and 'Earn' options, you should see quite a few options. Most non-Australian airlines don't have many ways to earn points other than flying (be it their airline, alliance or other partners).
Your only real options for non-flying based earn in Australia are Qantas or Virgin. AAdvantage is by far the best program if you're USA based or if you fly a lot on mid-level priced QF air fares on distances over 500 miles (AAdvantage only credits a minimum of 500 miles vs QF's 1000, and excludes some deep-discount economy fare buckets on QF).
My other suggestion is spend a few hours digging around here for information in the Qantas and Virgin/Velocity forums. There's a wealth of information here that may also assist in your choice.
And as others have mentioned, only having a temporary student visa is going to pretty much exclude you from any credit card (and especially the 'premium' cards that earn most points; even the Woolworths Qantas Card is actually a 'Platinum' credit card).
Some banks used to offer an option to earn FF points on a debit card, but they have all ceased (and were a very very poor earn rate, and you had to pay a high annual fee to opt in to earn).
IMHO you'd be better off getting an ING Orange Everyday Visa Debit card, which pays you $0.50c every time you withdraw $200 via EFTPOS (say take $200 out when you do your shopping). It's not a reward in points, it's a reward in cash
