I suggest Cypress, not treated wood. Use Titebond 3 glue, and outdoor wood screws in predrilled holes. Some treated wood is not smart to expose one's self to, others not so much. Arsenic (the "A" of CCA) is an accumulative toxin and once you get it in your system it stays and if you get enough of it you become a "former woodworker". Charles is right - don't waste white oak on this project - there will be better projects for that!
Also, Gorilla Glue is really strong, but can expand to misalign joinery - but this can be designed around. Good luck!
OPG3 Tweak everything!