How do you access Doze?
My wife's aging Note 2 has ADHD and drops serious battery since an errant 4.4 Android update. It comes and goes but mostly its always on.
Like Ry said, Doze is part of Android 6 and it seems unlikely that Samsung will update the old Note 2 to Android 6. I'm no expert but you might check for applications that might be causing the battery drain or do a factory data reset (back up first!).