Shultz,
Wow, what a cool idea! I have a 9 month old and am getting to the point of needing to build him a toybox. Perhaps I should pay you to build a second.....
You could use ramin dowels from your local building supply for the pegs; 3/16" or so and shave a taper into one end with a pocket knife to make them look authentic.
I'd probably start with 1"x1" boards for the posts and beams.
email me if you like, I think this is a great project and I'd love to help you plan it!
Shaun Garvey
Berkshire Barns