Pokey

My advice is don't do it. It's an incredible pain in the rear trying to navigate the process in my experience. Ended up giving up on it and selling before we moved. 

You're better off contacting a moving company to get an estimate of the cost. There's just too many variables to ballpark it accurately and every company should give you an estimate without charging you. For what it's worth, we've used 3 Movers before and had a good experience. I know they execute moves between Oz & UK a lot so they may be a good place to start if you're just in the pricing phase. Good luck with everything!

Good lord that sounds like a nightmare, both in terms of logistics and the financial side of it. 

That seems like an unbelievable hassle and the plant not even make the trip in good shape. And with the security issues mentioned by NicF, it's probably a no go. 

If they're flying dogs, just point them in the right direction and send them on their way. They'll be there when you arrive!