It is probably too late for this idea, but there is a new-ish type of lumber that most people haven't heard about. Several companies are now thermotreating/cooking inexpensive species of hardwood lumber, and it offers the same physical properties of the original hardwood, with the rot resistance of pressure treated softwoods, without the addition of chemicals. It also gives the wood a darker color, but you do have to put on some type of uv protector to prevent fading. It costs slightly more than pressure treated lumber, but it seems like it would be perfect for this dome application.
The big application right now is for decking and siding, but some people are also making furniture and even outdoor kitchens out of it. It is not commonly available everywhere, but it is started to gain traction in the U.S.
Full disclosure - I don't work for this company, but I did work on their website:
http://www.bingamanlumber.com/hardwood-products/thermo-treatment/page.aspx?id=1366