There are a large number of data sets that are open, that is available to be used without charge. The vast majority of these sets will contain quantitative data.
This is only a sample of what is available. It is better to search for data sets once you have a rough idea of your research topic.
The Australian government maintains a large database of open data.
The Queensland government maintains a good number of data sets about education, as does the NSW government.
You are probably familiar with the data available from the MySchool site.
The QUT library has a collection of education data sets from Australia and elsewhere. There is a link there to the Australian Bureau of Statistics education-related data sets.
Research Data Australia maintains a large database of data sets.
Globally there is a collection of databases about open data sets here. These are less likely to be useful other than perhaps providing contextual information for your topic. Jeremy Singer-Vine maintains a huge spreadsheet in which he has curated open data from a around the planet. More for interest than use.
The OECD also has very large collection of education related data.