Tips for wedding dress on plane?

I am getting married in Vegas this May. I live in Iowa. I need tips on the best way to get my dress there! I was thinking about taking it as my carry on and folding it in the compartment above our seats, and buying a handheld steamer to get any wrinkles out. I called my airline and they do not have closet space where I could hang it. The dress doesnt have any beading on it, but it does have a lot of pick ups. Any ideas would help!