IMO very reasonable, very achievable.
On your range outings I suggest a side-by-side comparison with a handgun of known performance, to better evaluate your own perfomance that day as well as that of the M19 and its ammo. A benchmark if you will.
For a comparison, my S&W Magna Classic would shoot into less than 1.75" at 50 yds from a rest, iron sights. I've had a number of common M29s that would shoot into 6" or less at 100 yds all day long. M41 S&Ws will do 2 MOA or less, all day long.
I seriously doubt you'll get that sort of accuracy from a non-fire-lapped M19 but IMO 6-8 MOA is a reasonable goal for you, from a rest. That translates into less than 2" groups at 50 ft from a rest.
Many, many gallery pistol shooters can achieve this level of accuracy from the offhand, it's not too difficult with a good 22LR.
FOCUS ON THE FRONT SIGHT ONLY! CONCENTRATE ON THE TRIGGER SQUEEZE! FRONT SIGHT, TRIGGER SQUEEZE!
Regards, Joe