Welcome to AFF!
Whenever I'm asked by a non-traveller about how to get into travelling, my advice is always the same: Go to New Zealand.
There is no easier way for a newbie to learn the ropes of international travel than to go to NZ. It's a magnificent country, easy and cheap to get to, with no language barrier, friendly people, spectacular scenery, great food, and endless things to do. Any time of year is a great time to go.
Given you have a family, it's also very safe and you don't need to worry about things like travel adaptors for power.
Go to NZ for a week or two (or three). Don't worry about points etc yet. When you come back, you'll officially be a traveller! And then you can start planning your dream family Europe/UK trip.
For what it's worth, if you want to go to Europe on points, Qantas points are just about your most difficult option. Focus on flexible points currencies and/or Velocity.