We work with large firms running TM on SQL servers doing replication to ensure consistency across the U.S. but we also work with solo's and small firms running TM on desktops. Keep in mind that Time Matters does need SQL server which will utilize about 1.5GB of RAM at almost all times. So having a desktop with a minimum of 4GB of RAM is advisable in a peer to peer environment.
When setting up the desktops make sure you have the Windows firewall and any anti virus set to allow both SQL and the Time Matters program files through on both PC's. Also make sure you set both desktops to be a part of the same HOMEGROUP and the same WORKGROUP. This will ensure you have correct permissions when the install is done.
Pick one PC to be the "Server" and install TM and the database. Then located the data folder and share that folder in the workgroup and homegroup. Then go to the 2nd PC and map that shared folder as a network drive and make sure you can copy a file to it and delete it. This is just a test for permissions settings. Then install TM on the 2nd machine.
You should be all set. A few things to remember in a peer to peer network. The "Server" machine must be on for the 2nd machine to work. Changing the Server machine's name or other network settings may cause disruption for the 2nd computer. Be careful of Windows updates on the "Server" machine as they can often make changes or reset settings necessary for the peer to peer connection to continue to work.
Read more on the Time Matters Support Blog.