I filed a child custody complaint. Mother of my child filed answer and counterclaim but has never served me. at court date can I get default judgement

You can raise lack of service, but a counterclaim does not normally have to be personally served.  Was it mailed to you?  Even if not, "default judgment" is not usually the outcome for service problems; if anything, it tends to result in an extended time to respond.  As a general matter, you should probably seek to address the merits, and not rely on procedural "gotchas," especially for child custody, as to which the Nevada Supreme Court has ordered that every decision must be based on the merits and not a procedural deficiency such as a discovery sanction.