I’ve made the drive to the coast (and up to Whidbey) from Seattle many times in my older Tesla, you’ll be fine. There are plenty of charging opportunities between Whidbey and La Push.

For optimal time efficiency, I suggest taking the ferry to/from the peninsula—this should save you a charging stop.

Anyway, you can use https://www.tesla.com/trips to get a good idea about whether or not it’s a good fit for your itinerary. This is just Tesla chargers. Superchargers are the fastest (and most expensive)