Hi Rohan, for such a short post you have covered many issues.
Firstly, there is certainly no reason why a person in Australian as the holder of a tourist visa cannot marry. The short answer therefore is yes, you can marry your Thai girlfriend in Australia.
Secondly, can she apply for a partner visa in Australia after you have married? The answer to this depends upon whether her tourist visa has the 'no further stay' condition (8503) attached to it. If it does then she can't apply for a partner visa in Australia. She must depart Australia prior to her tourist visa expiring and apply offshore, that is, back in Thailand.
If however her visa doesn't have the 'no further stay condition attached to it, then she can make an onshore partner visa application in Australia without having to return to Thailand.
To ascertain whether her current visa has the 'no further stay' condition attached to it, have a look at her visa grant notice and it will either make mention of Condition 8503, or it wont.
For more information on the no further stay condition, refer to this part of our forum: Condition 8503