How would you move a child-dragon (it's age is equal to a 8 years old child) to aplace to other if you were your legal owner and you want move it to a place to train it?

Hmm, let's see...

If the place you're sending it to is close enough, I imagine you'd just walk it there yourself. For locations farther away, it would have to be hauled in some sort of trailer. We've seen dragons towing cargo trucks in several episodes, so it seems there would be trucking companies you could hire to transport cargo or live dragons. Or people might have their own small trailers that they could hitch to their own adult dragons to transport things around. Depending on how far away it is, they just might use their own trailer and tow it there themselves.

So far, we've never been shown any form of transportation that doesn't rely on riding a dragon or having a dragon tow something. So there doesn't seem to be any other forms of transportation around other than that.