Looks to me definitely 60s-early 70s. If I'm not mistaken Kay used that badge in the mid to late 60s along with those style of tuners. I have owned two Kay's with matching badges, both and arch top and a 1965-67 "Plains Special". I have also owned Kays that do not have that badge, a 1940s Archtop, 50's flattop (debadged) but with stock Klusons and label, and a 1960s? Kay archctop with a factory pickup. Hope these help!
1965-67 Plains Special
1960s Kay Archtop I believe this to be late 60s-early 70s. Tuners if they were replaced or not, were stamped "Japan".
Hope these help! I can provide photos of my earlier Kay guitars if that would help. Still unsure how to exactly date them using date stamps (Harmony/Silvertone makes it really easy with a simple date stamp), so I find old catalogue ads. Old Kraftsman also shared the Kay designs as well as some True-tones I believe that might be worth checking out as well! Cheers!