Take all my changes on the current branch and move them to a new branch in Git

If you haven't been committing anything yet, you're already in the right position.

  1. Create a new branch: git checkout -b edge
  2. Your files haven't changed. Just git add what needs to and commit as usual.
  3. When you're done committing on edge, switch back to master with git checkout and git merge edge.

To add to JB's answer, if you have already started to make a few commits on master for what ended up as being a "edge" effort, you could:

git stash
git checkout -b edge master
git branch -f master SHA1_before_your_commits
git stash apply