Most of the birth records are in community lists and it would help greatly if you know the area of Newfoundland where she was born. One place to try is the FamilySearch database. They have her listed as Susan B Doyle and born in 1890. From the 1910 census in Rhode Island. You probably already have this info. She is listed as age 20 living with her aunt Ann Whitaway. It does not say she was from Newfoundland, just Canada. Ann’s father’s birthplace is listed as Ireland. You can view the entire record in FamilySearch. However the 1915 census lists her as age 22 with her aunt who is about 25-30 years older, still living in the same place.
The FHSNL has a birth database which is not complete and currently out of order that perhaps may have some records.
The Church of Latter Day Saints (Mormons) have research centers in a lot of cities where they have microfilm of vital statistics records. Its a hard way to do research but I did a lot of that in the beginning. They don’t have all of the records digitized yet either.
Short of that a visit to the archives in St John’s and looking at microfilms there is another avenue.

Have you thought about doing a DNA test. It has proven effective for me to find relatives both near and distant and some of them could have the information you need. There is bound to be a few of them doing genealogy too. There are Facebook sites for people interested in Newfoundland family research. That is for sure a more modern and less paper intense way of getting more information. I would try that while you are doing the other.

Also are there any relatives who could give you more info.

Hope this helps

Cathy Cavendish