If you're already using Github, then the easiest way to get both of you working on the same branch is to push/pull from Github continuously. Pushing / Pulling from each other's machines will get hairy quickly and result in a lot more headache down the road. Of course, you can use another in house server or set up a bare repo on one or both of your machines, but this will likely lead to an overly complex setup and cause a lot of extra time and effort in managing the source.
To get started between you (Dom) and another developer (we'll call him John) on the same branch, first create the branch on your local machine and push it up to Github:
#On Dom's machine:
git checkout -b cool_feature
git push origin cool_feature #assumes origin is github
#on John's machine:
git checkout -b cool_feature
git pull origin cool_feature
Now you both have the same copy of the repo on your localhosts. Develop at will and make sure both of you commit often and push the commits up to Github. Also, make sure you pull from Github often.