@LyonMartin
Standard way of doing it is
1. Start author server and do the deployment to author
2. Start publish server and do the deployment to publisher
3. Install the content packages and custom configs both in author and publisher. (In fact all the necessary pacakges)
If you want to repliacte the content, etc, conf path you need to setup the replication agent and then use the replication tree or content publish tree workflow.
But as this is your local setup i recommand way and easy way is to move the packages from author to publisher