You'll be fine. It won't be a question. Your registration from Utah was valid until it expired. Now just a matter or registering the car in WA. The only people who care about the time limits are cops.

When they say you have 30 days to register your car it means if you get pulled over and a cop asks you how long you have lived here and you say 9 months, they write you up for failing to register the car within the 30 days. Same for licenses. They have no knowledge how long you or the vehicle have been in WA unless you tell them. So get it registered. It probably won't even be an issue.