RCW 4.28.080 (Summons, how served) provides the various methods that service may properly be made on various entities. One method is "(15) In all other cases, to the defendant personally, or by leaving a copy of the summons at the house of his or her usual abode with some person of suitable age and discretion then resident therein." The statutes are at http://apps.leg.wa.gov/rcw/default.aspx?cite=4.28 .
Whether your 11-year-old daughter is a person "of suitable age and discretion" may be an issue. Simply being 11 may not mean that she is not "of suitable age and discretion". (A side question for you, why was your daughter at home alone if she is not "of suitable age and discretion"?)
The problem for you is that even if your daughter is not a proper person to serve, the attorney will simply hand you the appropriate notice in court and start the process over. That is, you may be able to delay the proceeding but you will not be able to stop the proceeding without the money to pay the rent and the fees.
In many counties, there are volunteers (many of them attorneys) who help tenants facing eviction. The volunteers generally can be found in an office in the county's superior courthouse. How much help the volunteers can provide depends on the facts of the case. The volunteers may be able to negotiate for you an agreement with your landlord. For example, if you agree to certainly move out by a specific date, the landlord may agree to not ask the sheriff to come by till the end of the month.
You should check whether there are volunteers in your county. As you likely know, evictions take place within days. You should not delay in finding help. The notices should tell you when and where to send your answers.