There are various methods of walking a tree: depth-first (children, then parent), breadth-first (parent, then children), and in-order (left child, parent, right child), top-down, and bottom-up are the obvious ones. The algorithm you describe is top-down; first the root node is processed, then its children, then its children's children... Offhand, I think that the approaches are all pretty much the same in terms of efficiency for dumping the tree. The only difference is the order in which the data comes out.

So the main consideration is rebuilding the tree afterwards, when your tied hash's STORE method is called over and over again. If you know what order you will be getting the nodes in, you could possibly optimize recreating the tree. For this, I think either breadth-first or top-down would be best; one of the orders that processes the parent before its children.