It seems plausible that it is the correct Kerstin.
In that case, this is her birth record:
https://sok.riksarkivet.se/bildvisning/C0041434_00028She is the daughter of Jacob Olofsson and his wife Anna Jönsdotter, born on the 10:th of October, baptized on the 11:th, 1804.
Here they are in the household examination record spanning 1800-1805, just after Kerstin is born:
https://sok.riksarkivet.se/bildvisning/C0041430_00079And again in 1806-1808:
https://sok.riksarkivet.se/bildvisning/C0041430_00097And here's a link to the examination record 1812-1815 (which you had a picture of):
https://sok.riksarkivet.se/bildvisning/C0041430_00130The notation regarding Jacob reads: "bevis utur Skredsviks kyrkobok. död." Meaning he had a proof of sorts from the church of Skredsvik (Bokenäs parish church), and also that he has passed.
Jacob Olsson dies on the 27:th of June 1813 of "magplågor" (stomach pains):
https://sok.riksarkivet.se/bildvisning/C0041434_00048But the notation above regarding Skredsvik got me thinking: It doesn't say "Bredvik" when Kerstin moves out from home, instead it is now obvious it reads: "flyttad till
Skredsviks". Now, Bredvik is a place in Bokenäs parish (in which the church is called Skredsviks church), so it was just a very strange coincidence that your family happened to be there, and which got me almost certain it was the correct Kerstin. Now, I'm not so sure, but still it seems plausible.
The Kerstin we know for a fact is your ancestor, which is present in Bokenäs, still has two different dates of birth. On the first record she is noted as being born on the 10:th of April 1804. Then in the later record, she is noted as being born on the 10:th of July. So clearly there is some confusion as to when she was born.
One way of solving this would be to try to find an estate inventory made after the death of her mother.
Here's the marriage between Elias Olsson and Kerstin Jacobsdotter:
https://sok.riksarkivet.se/bildvisning/C0039945_00080