There is no "gun registration" in Washington.
If you buy a handgun the purchase is run through the regular federal NICS and it is also run through various state agencies by the local law enforcement agency.
There used to be a voluntary "Pistol/Revolver Private Disposition/Transfer Form #652 004" that a private citizen could use to document the transfer of a privately owned handgun.
It's no longer in use since the "universal background check" law went into effect.
There are many many many assfucked shitstained retarded shiteating nutlicking asswipe know-it-all's who will spout this bullshit.
For further reference please use the the following format when asking a question:
WHO
WHAT
WHERE
WHY
WHEN
HOW
Who: Your daughter (was told by who that she needed to register her firearm)
What: Told she needs to register her handgun
Were: Where was she when she was told that
Why: Why was she told that
When: When
How: How did her firearm become a topic of conversation
It appears you gave the firearm to her before she became a Washington State resident - She's golden.
http://app.leg.wa.gov/rcw/default.aspx?cite=9.41.113