I am looking for information on the Rae shipping family Kirkcudbright/Liverpool in early 1800s.
About 30 entries for that surname born Scotland living in Liverpool. No names or birth years given in your post as to which particular Rae's you are referring to so how can any connection be established to Alexander?
This seems to be the 1851 entry for Alexander - all b Kirkcudbright
William Kerr 37 joiner b Minigaff
Jane 34
John 10
Elizabeth 7
Alexander B 5
William 4
Gorden 1
Alexander Rae 71 father in law annuitant
Hugh Coltart 20 apprentice
Sarah Henny 25 servant
Mary Beek 16 servant
Source Citation
Kirkcudbright ED1 Page 19 Line 15
In 1841 - Alexander is an Innkeeper
Why do you think there is a connection? You need to supply more information