Hey there
We are also new to Washington. Our son is 5, so our kids are different ages, but I know what it's like to move and not know anyone. We moved once when our son was about a year old and it was miserable because I didn't have any social outlet. I loved staying home with our ds, but he wasn't really a very good conversationalist at that point.LOL
This time around the move has been easier. Washington is a really friendly place. I've already met a couple of friends and ds already has friends to play with.
I don't know anyone with a 2yo, but do know a young girl with a baby. My other friend here has a 4yo ds, and 6yo dd.
PM me if you want to talk.