Do I need a separate server for Quorum?
Couple of points of clarification. Nodes and replicas are not the same thing. Nodes refer to the Windows Failover cluster and replicas to AvailabilityGroup instances. So assuming you are running a 2 node WSFC, each hosting a SQL instance in an AvailabilityGroup, then yes, you will need another server to achieve quorum and avoid split brain behavior. The easiest way to achieve this is simply set up a quorum file on another server outside of the cluster, known as Node and File Share majority. Read more on WSFC Quorum Modes.

You don't necessarily need to commission a new server for this.  Any server outside of the server will work.