There is tons of land where you can do dispersed camping. No one’s probably going to give you their coordinates of their favorite spot but if you just buy a Washington Gazetteer look at forest service type roads and figure out who has jurisdiction over land, you can get a good idea of where there might be dispersed camping. You can also view the sites with satellite images and see evidence of dispersed camping.

Having an almost reformed reactive dog, I feel your pain just make sure you have control of your dog because even if you’re dispersed, someone or some thing could come into your camp at any time.

Good Luck!

https://www.wta.org/go-outside/new-to-hiking/camping-101/how-to-dispersed-camping-on-public-lands

https://www.rei.com/b/delorme/c/paper-maps