Smart Move! I believe it is the schedule that will do what you want and I doubt firmware fixes it as not even brand new Dahua cameras have the feature working the way it should!
A common theme around here is don't fix what ain't broke. If the unit is working and meets your needs, in many instances an update breaks what you had working and provides you with something you didn't need. A Z12E that someone updated and then constantly reboots comes to mind, and a certain PTZ that loses autotracking with an update come to mind, a Hikvision ANPR camera losing half the FPS and ability to read US plates - those are big deals to have happen. Don't do it unless it is fixing a problem you are experiencing or adds a feature you really need.
Further, it is best to obtain any firmware updates from the vendor you purchased it from so that you do not run into issues. Any firmware you find here or elsewhere is obviously proceed at your own risk. We have many threads here where someone tried an update with a firmware they found on the internet and bricked their unit.