Yes, Doha might be a rather small town, BUT traffic at peak times is horrible. I suggest you get places for your children in school and then select housing based on proximity to the school. It often takes me 45 minutes to go from West Bay to Al Waab.
No Australian school in Doha. There is a Compass school, many others go to DESS, Doha College, Park House and American School of Doha. Contact info for them and many other schools located under the tab at the top of QL "Qatar Guide". You will need to apply to several schools as spots are hard to find.