Sure, plenty of ways.
1) You can save the report as a PDF and dump it to a specified directory with a date / time stamp as part of the file name.
2) You can create the report as an HTML document and store it in a record as text data.
3) You can create a separate table in which you store all the relevant data in appropriate fields, and generate the report from there.
Just a few ideas off the top of my head. HTH
Re Mike's option 3, if you need to keep everything internal to FileMaker: setup a change log table, where a separate record would be entered and time-stamped for each change/creation instance of each calendar entry. Then you can build a reporting system based on that table and date ranges to recreate a shot of the calendar as it looked at any given time.
Warning: a lot more work than actually grapping snapshots per options 1 and 2, but 3 would allow you to build historic reports for dates/times without having had to actually run the reports and save them in real time, as 1 and 2 require.