On Friday the movers came and packed up a full 20 foot container for my move from Boston, Massachusetts (north east USA) to Napier, New Zealand. We are 2 adults, 2 kids, without too much furniture. We have 4 beds, 1 couch, 1 dining room table plus 6 chairs, lots of books, lots of games, lots of CDs, DVDs, lots and lots of stuffed animals and toys, and lots of kitchen stuff (dishes, pots, pans, glasses, mugs, etc.). There was a little room to spare. All in all, it should end up costing us just under $10,000 in US dollars. That includes insurance. But obviously, it's going a lot farther than your stuff will go, so I'd say you've gotta come in well under $10,000.
Have you checked out movingscam.com
? They have a lot of good info, mostly for US moving, but it might be helpful.
Good luck! Where are you moving to?