Sometimes people were taken back to their own parish for burial, sometimes they were buried in Northampton. I've seen both.
A young married woman might be taken back to her parent's home parish; and there's always the Nonconformist burial gounds, which don't always have records.
I have to say, I can't see Sarah Hakes anywhere, but when I checked Piddington, there were no burials listed at all from July 1812 to Dec 1812. Did wonder whether they'd managed to miss her off, or alternatively, whether the Baptist church in nearby Hackleton has a burial ground.
Investigating Hackleton, it seems that they did have a burial ground, but they didn't have a register until 1814. While they did record some of the previous burials, the register say, "The names entered in this book before Dec 14 1814 were persons whom the sexton, or their relations, remembered being buried. There had been others buried, but no particular account could be given of them"
If they were attending, however briefly, the Baptist church, that might account for not only the lack of Sarah's burial, but the lack of a baptism for her child as well, as a similar situation applied for the births listed in the Births Register.
