can you travel from europe to australia by boat

Yes you can.

You could contact the Merchant Navy and see if they have any
paying berths on any of their boats.

The usual cruise liners wouldn't do a direct boat to
Australia but they could link you up. This would be a more
expensive option than the Merchant Navy.

Depending on how old you are, there are Tall Ships that
sail all over the world, but you have to work on them
as a sailor, putting up sails, scrubbing the deck, working in the galley and so on.

Finally, some of the big shiping lines may have paying
berths. If you like the company of Phillipino sailors, you'll have a great time!

If you want to travel in style instead of bunking up on a merchant ship, there are quite a few cruise companies offering “round the world” trips that enable you to buy separate sectors. Such as these from Sega or Cunard (see links below). Be warned though, it takes about 50 days and costs from £5000. For other examples, search for “round the world cruise” in Google and look for ones that sell separate sectors. If you want total opulence, the Cunard Queen Mary 2 is making her first round the world cruise later this year.

http://www.saga.co.uk/travel/cruises3/critinerary.asp?itineraryID=F3217B68-BE58-... copy, England&portToName=Sydney, Australia

http://www.cunard.co.uk/CruiseItinerary_tab.asp?cruiseid=2864&LeftNav=Planne... copy