Had this problem a few years back. 4 dogs chased a doe across my property and couple days later saw them chasing another in a field nearby. Called wdfw and reported. Was asked if I knew who owned them (I didnt) and was told I could destroy them if they chased again on my property. Warden also told me it was a big problem in our area and had reports of several fawn kills attributed to domestic dogs. Found out later that some of the other locals had taken care of the pack, at least two while feeding on a downed deer. Domestic dogs running freely in deer country is not good , let your conscience be your guide as to how you'd handle it.