It used to be the case that you could but I haven't read up on the changes made from 7th October this year.

http://www.citizenship.gov.au/
http://www.immi.gov.au/legislation/amendments/index.htm

You can apply for a “Spouse Visa: Onshore Temporary (Subclasses 820) and Permanent (subclass 801)”. This entitles you to stay in the country for two years on a temporary basis. After this you can apply for a permanent visa or Australian citizenship.

If you are not granted leave to stay (such as if it is considered the marriage is not genuine (a “marriage of convenience”), you will be required to leave the country under the terms of your tourist visa. You can then apply for a “Spouse Temporary Visa (Subclass 309) and Permanent Visa (Subclass 100)”. This is for people from overseas to enter and stay in Australia with their partner, who must be an Australian citizen, Australian permanent resident or eligible New Zealand citizen. If two years after you apply the spousal relationship is ongoing, a permanent visa may be granted.

Follow these links:
http://www.citizenship.gov.au/applying/spouses.htm
http://www.immi.gov.au/migrants/family/family-visas-partner.htm
http://www.immi.gov.au/migrants/partners/spouse/820-801/index.htm
http://www.immi.gov.au/migrants/partners/spouse/309-100/index.htm