Ruger's site is somewhat inaccurate, especially for the Single Six guns. According to John Dougan's book "Ruger Pistol and Revolvers" your gun was made in 1959.
If it is within a year or two... you are good to go . No need to know the exact year/month/day hour:min:sec that it was completed ... At least I am 'okay' with knowing around the approximate year.
Where you can get tripped up is with clean-up guns. For example I have a 'low' serial # fixed sighted ROA, but it was actually sent out the door years later....