Washington provides for Domestic Violence Orders for Protection. (In Ohio, where I practice, we have a similar procedure.) The court should set a hearing date, at which point you (and your child) will tell the court precisely what happened.
True, the more information you submit, the more information with which you can establish grounds for a restraining order. But your in-court testimony should suffice.
My experience in Pierce County Superior Court is that to obtain a domestic violence restraining order, you need to make clear and specific allegations while under oath that you have been a victim of domestic violence in the past and that you are afraid the conduct may continue in the future. Any evidence that you have will be helpful in persuading the judge - for example photographs, emails from the respondent, declarations from witnesses. The fact that your child was present during the incident will likely carry great weight in the judge's mind. However, even if there is no evidence other than your sworn statement, the order can still be issued. Don't be afraid to appear at the hearing because you think you don't have enough evidence. If your statement and your evidence are persuasive, the fact that the order may negatively impact the respondent is not a persuasive defense. Pierce County has some excellent resources for victims of domestic violence which are available at no cost. Contact the YWCA or the court clerk for more information.