Lesley, in the IGI Isabella (or Elizabeth), if illegitimate, will be entered under her mother's surname, whether or not her father was recorded at her baptism, and even though the parish register does not usually give a surname to the child.

As Frances said, the usual format is to write Isabella illegitimate (or base born, or base child) daur of (father's name) and (mother's name) - or just daur of the mother's full name.
Even if only the mother's name is given at baptism, in the IoM the child would usually be known in censuses etc. by the father's surname.

It can be difficult to find the child in the IGI because of this, if she is known by her father's name and the mother's name is not known. Sometimes he/she is with relatives in censuses, and sometimes they are mentioned in the father's or grandparents' wills.

If Isabella's mother was Margaret Clague, her bapt should be under Clague in the IGI. If it isn't, I suggest you ask whoever gave you the information what this is based on.

You could try looking for all Isabellas or Elizabeths in the IGI for around the year she was born, looking for an illegitimate entry, but the IGI will only accept searches with no surname if a batch number is included. You could try her forename with all IoM batch numbers in turn, and list all the possible illegitimate bapts for her. You may find father .... Cowle on one of them, if that was the name she was known by. http://freepages.genealogy.rootsweb.com/~hughwallis/IGIBatchNumbers/CountyIsle_Of_Man.htm#PageTitle

Sue