OP wise choice IMO. You have to factor that with young DC's and a very hardworking DH, you will be carrying the can with the childcare.
Resentment builds in this scenario and as you have no friends/family nearby to vent, it does get worse. No matter how much you love each other. He is fulfilled, you not so much...
Even if he DIDN'T stop you leaving with the children (IF the worst happened) you would be back at square one, in London? with a husband and father in Australia.
Not a good scenario.
Considering the (absolutely normal) strain and stress moving to the other side of the world with tiny DC's, this would put on your marriage, I really am pleased you are considering not going. 
Of course, it could all be a bed of roses in the blistering heat, days away from home, with small Dc's, but I think not.
I can't leave my country, my husband would gladly let me take DD, I imagine. (I do all childcare) But where would I be? In the UK with no job, DD with no school and out of her settled way of life and school and friends and an absent father.
Married 16 years, thought it would be amazing, we loved each other dearly, but it all crumbled after 10 years here. Husbands country. Nightmare situation to be in and I am lonelier than I can possibly describe.
These are not horror stories, they are what happens, sadly, when you are the 'trailing spouse'
You sound like you have a great life now!