If you have access to a shared directory, you can (see git clone and git remote):
git clone --bare /path/to/your/laptop/repo /shared/path/to/desktop/repo.git
git remote add desktop /shared/path/to/desktop/repo.git
That will create a bare repo, referenced in your local repo as “desktop”.
Since it is bare, you can push to it (as well as pull from it if needed)
git push desktop
As the ProGit book mentions, git does support the file protocol:
The most basic is the Local protocol, in which the remote repository is in another directory on disk.
This is often used if everyone on your team has access to a shared filesystem such as an NFS mount, or in the less likely case that everyone logs in to the same computer.