Initial Steps for Dissolving a Domestic Partnership
You should consult with an attorney. The meretricious relationship case laws are still in effect; these can lead to differing results to that of a "marriage". The forms necessary are available through the Washington Courts system.
Filing and Dissolution
Prior to 2006, two separate actions were necessary if children were involved in a "meretricious" relationship. Same Sex couples having children had to engage in two separate actions- a civil action for the division of assets, and a "domestic" action regarding any children. This process has now been coupled together so a single action needs to be filed as a domestic matter.
After June 12, 2008, uncontested domestic partnerships can no longer be dissolved simply by filing paperwork with the Secretary of State. These partnerships must now be conducted through the court system, much like a divorce.
Additional resources provided by the author
The Washington State Courts system has many of the pattern forms you need for dissolution with or without children.
For a good guide on the process involving dissolution in general, the NW Women's Law Center gives great advice and information.