I went to school in WA state last year, and as such i studied up a little on the laws of Washington. It is legal for you to carry a loaded firearms on your person if participating or going to or from a firearms related venue (collectors meeting for example), out door activities, in your fixed place of residence, or in your fixed place of business(job).
here is Washington code relating to firearms
http://apps.leg.wa.gov/RCW/default.aspx?cite=9.41
while it is difficult for an under 21 year old to carry a HG, it can be done, as mentioned by gaarry if it is unloaded and closed in an opaque container. I beleive harbor freight sells one that may work if you are interested.
contrary to what gaary said however, you cannot buy handgun ammo if you are under 21, according to federal law, online. Idk how they verify it however, as ive never tried to do so.
and im wondering about that as well, as there are 9mm, 40sw, and 45 acp carbines and rifles, so can you buy those if you say theyre for use in a rifle? any one have answers for that?