Hello Sue and Philip
I've found a possible mother for Emily b 1851, the posthumously born daughter of Robert Joughin, miller.
As you suggested, Sue, I looked through the IGI for births of an Emily in Douglas, and I noted down the illegitimate ones. Then I looked at the 1861 census index to see if those illegitimate Emilies were with the mother named in the IGI.
An Emily Morrison was baptised to a mother Ann 21 Dec 1851 Douglas St George, and there was no 9yr old Emily Morrison with a mother Ann in the 1861 index (of course, Ann might have married in the meantime and they could have been entered under a different name, or Emily could have died etc). The thing that leapt out at me was finding an Ann Morrison , servant, in 1851 on the next census page to Robert Joughin !
1851
Braddan 2/15
household 55
Ballaughtin
John Kermode head mar 25 miller's cartman b Malew
Isabella wife 26 b German
John son 2 b Braddan
George son 1 b Braddan
Ann Morrison visitor unm 22 house servant b Arbory
Braddan 2/16
household 59
St Helena Cottage, Ballaughtin
James Cowin head mar 38 miller and corn dealer emp 11 men b Lonan
Maria wife 34 b Lonan
John J son 3 b Braddan
Eleanor Kewley serv unm 20 house servant b Lonan
Robert Joughin serv unm 21 journeyman miller b Braddan
Catherine Kewley serv unm 11 nurse b St Anne
(probably James Cowin and Maria Looney ?)
It would be interesting to see the actual baptismal record for Emily Morrison. Don't they sometimes have the name of the baby's father noted in the margin ?