It will likely be treated as a motorcycle in the State of Washington since Whizzers are over the 50cc limit prescribed by their laws, as 50cc or less would qualify as a moped.
This would mean a motorcycle registration along with a motorcycle endorsement on your drivers license...Last I knew, insurance wasn't required on a moped or motorcycle in Washington State but the laws on that may well have changed...If you have motor vehicle inspections in your state, that would probably be required as well.
I would be making a phone call or visit to your local DMV for further details.