You want to email the entire log file? This is not possible.
You can however push the logs else where (to an FTP/HTTP/HTTPS server).
The monitoring log has its own log rotation settings just like the access.log, so yes you can adjust the settings as you desire.
This log file should only contain entries for a particular user defined category, and shouldn't be very large, That is why I wanted to know if we could rotate it once a week and send it off in an email, so it sounds like that isn't an option but I could rotate once a week and ftp or http it to a webserver.
It is true that the logs are small, but the problem is that logs are all transactional, so they are written when a specific transaction takes place. This only leaves the pushing settings to send information like the logs.
Otherwise you could just trigger an event to send an email each time a specific event/transaction takes place (which is a disabled rule in there by default).