The Australian tax year runs from 1st July till end of Jun 30. So if you planning to arrive around october time, then they will want to know what you have earned in the UK since 1st JULY....both of you.
The other thing to bare in mind is your older child. If he decides to get a part-time job whilst studying......and earns over a certain amount (not sure what it is...think around $11K)....you will not be entitled to FTB for him.
Many people have been caught out by this.........i know people who have had to pay back thousands as it was assumed that being in fulltime education gives you the right to claim...yes it does...but once that child earns a certain amount...you are not...
My eldest daughter worked part-time whilst studying.......we opted to defer claiming for her until the end of the financial year. We could then see how much she had earned....if she was under then we made a claim. They then pay you a whole years worth in one go for that child.