If you travel the world, the country, or the area, you go to many different places in the world or in a particular country or area. If you travel to a place, that place is your ultimate destination.
He has had to travel the country in search of work. (he's had to travel to many different places there)
I traveled the world gathering material for my book. (I traveled around the world)
You'd better travel to Los Angeles tomorrow. (you'd better go there specifically)
So, if you want to say that Australia is the place where you choose to go, then say "I will go to Australia" because that's your destination. If you want to stress that you'll be traveling all over the country, "I will travel Australia" is just right.