I'm surprised your agent wasn't able to help you with this.
With that said, I would not suggest a flight that early and here's why; normally, your ship is scheduled to be in port by 8:00am. Given that they arrive on time and begin disembarkation on time, normally the very earliest anyone will leave the ship is going to be 8:30 - 8:45am. So for argument sake, let's say you are one of the first ones off and you disembark by 9:00am. Although it can take as little as 30 minutes to get to the airport, I would allow at least 45 minutes to an hour.
So, if everything came together perfectly, you could possibly be at the airport by 10:30 and given that you need to be at the airport around 90 minutes prior to the flight, you might get lucky and make it on time.
But you have to ask yourself; do you feel lucky? Well, do you??
To be on the safe side, I normally tell people leaving from Seattle not to book a flight before 1:00pm, which will give you a little more leeway should any delays occur. Personally, I prefer not to have to worry and rush, but if you decide you want to take the chance, then I would suggest you seriously look at purchasing travel insurance.