That's right, Peter Hansen Møller is a candidate to be the father of "your" Christopher, who was yet to be born in 1787.
Born about 1790, and living in England by 1814, your Christopher can only appear on one Danish census - 1801 census.
Earlier Karsten found this candidate for your Christopher.
Name: Jens Christopher Møller
Christening Date: 10 Apr 1791
Christening Place: Holmens Sogn, Copenhagen, Denmark
Father: Peter Hansen Møller <---------------
Mother: Bodil Nielsdr <-----------
The boy above could be born in 1790, but anyway, close enough so that his age is consistent with the age in the England census. Usually census records are not "right on the money."
Below is a Peter Hansen Møller in Copenhagen in 1787 with a wife "Bohle" (probably Bodil, since there is no such name as Bohle).
København, København (Staden), Øster Kvarter, , Laksegade 305, 1, FT-1787, C1091
Peter Hansen Møller 44 Gift Manden Skoemager Mester
Bohle 40 Gift Konen
Kisten 20 Ugift Søster Tiener (a sister, not a daughter)
Hans Peter 9 Ugift ældste Søn
Anna Kistine 8 Ugift Datter
Joachim Peter 6 Ugift Søn
Same family in 1801. Now the father is a widower:
København, København (Staden), Øster Kvarter, Øster Kvarter, Matr. 310, 922, FT-1801, A5021
Peder Hansen Møller 60 Enkemand Husbonde Skoemager Mester
Anne Christine Møller 21 Ugift hans Datter
Jochum Diderich Møller 20 Ugift hans Søn Skoemager Svend
Søren Peter Møller 16 Ugift hans Søn i lære
Anne Sophie Møller 12 Ugift hans Datter
Jens Christopherier?? Møller 9 Ugift hans Søn i lære <------
To clarify, none of us - Karsten or me or you - can say whether or not Jens Christopher Møller is your Christopher. These records are not for the family tree - they are for the shoebox in this hunting stage only.
The next step is to find Peter Hansen Møller's son Jens Christopher in later years. If he stays in Denmark when your Christopher is in England, then we can rule him out.
Then one goes on to find more candidates and rule them out.
One also looks for correspondences between Christopher in England and the candidates in Denmark. For example, if your Christopher lives next door to a Jochum Diderich Møller, that could be a clue. Or what if Jochum goes to England and Anglicizes his name to Jacob, and uses the patronymic Petersen? Then a Jacob Petersen in the records for your Christopher could be a clue (for example, a witness at a wedding, a baptismal sponsor, a neighbor, etc).
For this reason, the more records posted from England, the better. I tried to start that a little above. If you can add more transcriptions - great.
The above Danish records are taken from a very easy-to-use website called Dansk Demografisk Database at www.ddd.da.dk
. When searching, use wildcard %
To search for Caroline in Copenhagen, consider Karoline, Karolina, Carolina, Lina; or perhaps she could appear with only her middle name of Augusta, Gusta, etc., or her name could appear mangled in the transcription. I have searched for a girl of that name in Copenhagen in 1801, but perhaps you'll have better luck, or you can expand to other areas of Denmark.