I have had a look at some of the records.I am sure that Caroline is at least related to Isaac and Jane Prior but figure that she is their fourth child of seven children. The first being born on the ship in late 1841 or just prior to their departure.
I had a look at Caroline's death and see she died one week after giving birth at Upper Skilly which is where Isaac was teaching at the time.Her death record says she died at McLaren Vale which I find strange as it means she would have had to leave Upper Skilly straight after giving birth in the middle of summer on a journey which would probably would have taken a week. I would imagine she died up north and her death registered later when her husband returned home.
As for a record of Caroline's parentage, have you checked the church records in McLaren Vale for baptism records (Baptist Church).Other than this there may be school records at the Meadows school which used to be the Kondoparinga school and there was a Isaac Prior as the teacher there in 1859-1861 McLarenvale school1861 1862 .Other school Isaac taught were port Wakefield school 1867, 1868.He then taught at the Lower and Upper Skilly schools 1870 to 1878. then Arthurton School 1880.