I don't think full time or part time course makes a different, as long as you graduate and get your degree. And after you graduated, you have to leave the country when you apply, my friend's sister has gone to Fiji for 1 week when she applied.
You can apply for skills immigrant, it is a point system. You have to look at the immigration website for details, and it change from time to time. But the method is as follows:
eg. age 20 to 45 has 15 points, fluent English 20 points, undergraduate 15 points, postgraduate (depends on the subject) another 10 points, work experience (depends on the kind of work) 25 points, close relative in Australia 10 points etc. If your total is above a certain level then you are more likely to be accepted.
http://www.immi.gov.au/immigration.htm
https://www.migrationexpert.com/register.asp?type=1