The first RN# (registered identification number) was issued in 1959 (and the number was 13670, FYI). Thus, the dress can't be older than 1959. My special secret RN# formula of:
x (your garment's RN#) - 13670 = y/2635 = years to add to 1959 to get the oldest your garment can be
Thus, 17555-13670 = 3,885/2635 = 1.5 + 1959 = 1961 or so
It's not absolute or exact, but it's pretty accurate.
That does not mean, however that the dress is from 1961 or so, only that 1961-ish is the first time that label was used, so the garment cannot be any older.
If the company went out of business in the 60s, as Victoria suggests, then you can definitely say that the dress is 60s.
FYI, Dacron was invented by DuPont in the very early 1950s, and is still made today, so that's not much help here.