Is this the shipping manifest entry you have:
Departure Place: Londonderry, Ireland
Arrival Date: 7 Dec 1853
Arrival Place: Philadelphia, Pennsylvania, USA
Ship: Envoy
Rebecca Hunter, 25
Sarah A., 10
Robert, 8
Joseph, 6
Martha J., 4
Hugh, 9 Months
Just a possibility, but a Sarah Ann Hunter was born on 2 September 1843 and was baptised on 1 October 1843 in Drumachose Presbyterian Church in Limavady, County Londonderry. Her parents were recorded as Joseph Hunter and Rebecca George of Ballyquin.
Ballyquin townland:
https://www.townlands.ie/en/londonderry/keenaght/carrick/fruithill/ballyquin/
I am a little wary of the entry showing a 25 year old Rebecca with a 10 year old daughter on the shipping manifest. This means that she would have been 15 when she married. This did happen of course. A father's consent would have been required.
I wonder if
1 there has been a transcription error mistaking a 3 for a 2,
2 that Rebecca, if the 1822 certificate is correct, would have been older than her husband and has adjusted her age accordingly.
3 her husband has been married previously and the oldest child, at least, is his child by a former wife who has died.
The differences between the manifest and the children listed on the Findagrave records is worth investigating
Sarah, Robert and Martha do not appear yet they arrived with Rebecca George Hunter. Joseph does appear and his birthdate seems to tally with the manifest. Hugh does appear but his date does not tally with the manifest. He is shown as being born in 1853 (presumably in Ireland) on the manifest but 1851 on the Findagrave record.
I wonder if there were two families. Joseph being the only one of the first family who kept in touch
Then again Sarah is the name of Rebecca George Hunter's mother so perhaps an early marriage was possible or that Rebecca was born on 1822 rather than 1828.
Perhaps Sarah, Robert and Martha had died after arriving in the US. Though I note Joseph had a daughter Martha born in 1877.