When one party breaches the other party always has a duty to mitigate their damages. Here, that means your landlord has to get a new tenant. In my experience, a court will allow the landlord to take one additional month's rent, but not more.
But the question of whether she can keep your entire deposit turns on what your rental ageement says your deposit is for. If it is a security deposit, to secure "all" your obligations, then possibly yes. If it is a damage deposit, and you didn't damage the place, then possibly not. No attorney can tell you for sure what a contract says without reading it. And no attorney can accurately forecast what a judge is going to do.
But I have seen literally hundreds of leases in WA that contain terms that are utterly unenforceable, and landlords who believe they can enforce these agreements. Landlords have this unfortunate tendency *not* to read the law, which says that leases that contain terms inconsistent with the RLTA are not enforceable. See RCW 59 18 230. The lease terms that are consistent with the RLTA are enforceable, the other terms are not.
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Your question has an important contradiction in it. You said both that you gave notice you are moving and that you are staying until the landlord finds a new tenant.
You are not required to live at the unit, only pay rent and not cause damage. If you move out early, your landlord is not damaged as long as you continue paying the rent. Once you vacate and return the keys, the landlord has a duty to make reasonable efforts to find a new tenant. RCW 59.18.310. You are liable until the end of the lease, until the landlord finds a new tenant, or until, through reasonable efforts, the landlord would have found a new tenant. If you keep paying rent until the landlord finds a new tenant, the only money the landlord could recover is for damage or cleaning costs.
As long as you remain in possession, the landlord is not required to find a new tenant.