Upvote:1
A friend of mine has recently moved to Australia for 12 months on a 408 visa, so I can give an answer.
I'm assuming we'd need to apply for a separate tourist visa in order to do this. What visa would be appropriate?
When your TSS visa is issued, it will be valid from the date of issue, rather than from the day when your contract begins. This would allow you to immediately travel to Australia without getting extra visas. I'm assuming you have applied for the TSS visa together with your wife, so you should all receive the visa at the same time.
It is also common for the visa to be slightly longer than your contract. In my friend's case, she was issued a 13-month visa for her 12-month contract. This should give you another month of free time after the job is over.
Would we need to do anything like leave and re-enter?
Unfortunately I have no idea how it would work if you had a separate tourist visa. Hopefully someone else can contribute. However we have a related question on staying on a tourist visa after your work visa ends.