She is probably the daughter of the John Gater, wife Mary, who lived in Lamberhurst, Kent, England *and stayed there*, never removing to America.
Examination of the original Lamberhurst parish register showed the following:
1. John GATER had a daughter Elizabeth bap. Dec. 1632 [exact date not viewable on the microfilm
2. John GATER and wife Mary had a son John bap. 5 Mar. 1634. [1635 Gregorian calendar]
3. John GATER and wife Mary had a son William bap. 20 Mar. 1637 [1638 Gregorian calendar]
"Gater" apparently was not that uncommon a name.