Going by the longer list of names from that link for children to James and Janet, and from the name Stevens mentioned earlier, is this Janet's entry, submitted on IGI:
JANET DUNLOP Birth: 20 NOV 1808 Fenwick, Ayr, Scotland
Parents:ANDREW DUNLOP and MARGARET STEVEN
That is definitely her - I've found the same entry at SP. I'm more convinced now that the other 3 children I've found are their children due to the names and the timing of the names; 1st child Margaret after Janet's mother, 2nd child Janet after James's mother, 3rd child Adam after James's father, 4th child Andrew after Janet's father, 5th child James after James. It seems like a classic case of Scottish naming.
I'm further convinced because I have found James and Janet on the 1841 census in Fenwick with children Andrew (aged 10), James (aged eight) and Mary (aged 2) - there is only one James Dunlop born in Fenwick around that time and that was 1835 to Margaret and Matthew so the Tarbolton born James looks like he must be James and Janet's son. Of the children missing I assume the Tarbolton born Mary died young for them to have named another child Mary, Margaret is old enough to be married or working elsewhere, Adam is with his grandmother and Janet must either have died young or be out working somewhere by the age of 13 (I suspect she died though as I can't find her on the census at all.)
It looks like MIs might be my only hope in dating Janet's death. I've found a couple of certificates on which a mother or father of the bride/groom is not listed as deceased when they were; Is this quite common? I hadn't thought about the Mitchell so that might be worth checking. Thanks again for the enormous help.
Regards
Michelle