230v -110v
Yes, there are converters, although they are usually designed for 1 component usage only. Don't know if there is a 'whole house' converter available. As I understand it, there are 3 factors which need to be accomodated: the plugs, the voltage, and the frequency.
One option is to have some form of converter which you plug into whatever is available in European and Australian campgrounds and puts out 110V 60 cycle power which the trailer then plugs into. If this is feasable, the only problem is you cannot use any European or Australian appliances inside the trailer, which is wired for and powered by 110V 60cycle. There are probably individual unit converters which would convert the US power back in to European/Australian which could get around this problem.
A rather more involved solution is to rewire the trailer to run on European/Australian power (including the appropriate outlets inside). Then hardwire an individual converter inline with each built in appliance. This is non trivial, and would be a challange to accomplish between the US and European legs.
Speaking of which, how do you plan on getting the unit from the US to Europe, and from Europe to Australia? As far as I know, there is only 1 RV which can travel on water, and no trailers
What will you be using for a tow vehicle for each leg? How will you get the unit serviced?
It might be cheaper in the long run to rent the unit in each area, and buy the one you want in Australia, already set up for that area.