@Lori Spitz‚ What Matt said here would be the quickest solution. Alternatively you could simply set up the entire year's worth of projects at once and set them all up with the right dates for each month.
We do have an case in our world where we can forecast work for the year, but don't want to really build the projects themselves until 2-3 weeks before the work is due. In that case there's one project with a set of tasks for 'Build project' that have all the right dates forecast for the client deliverables. Something like that could work for your team maybe. Set up one master project that's just a recurring task for 'Go build this project' and have it remind them monthly.
As you explore Fusion, there may be a solution in there though to have it watch for a particular trigger and automatically go create the project for the next month for you.
Katherine