To the best of my knowledge, Suzanne, and I don't believe I'm wrong, the only nursemaid travelling on the 'Titanic' was Alice Cleaver, who attended the Allison children, Lorraine and Trevor. Famously, Lorraine Allison was the only child from first-class to perish, along with her parents, Hudson and Bess. The circumstances of Cleaver's rescue with baby Trevor have been picked over ad nauseum on the board over the past few years - I won't go into all that now but, suffice to say, she can't be the woman you're looking for.
It is possible that one of the female victims in either second-class or steerage had been working as a nursemaid, or was going to America to take up such a position, but I can't offer you any names. I've certainly never heard of such a woman, particularly one from Scotland, but that doesn't mean she didn't exist!
There was also Elizabeth Burns (nursemaid to Robert Spedden) and (in 3rd Class) Elizabeth Dowdell, who was caring for Ethel Emanuel. But these were survivors, and both American. There were indeed a few others who had worked as nurses or nursemaids in the past or had plans to do so in the future, but none that I know of who were among the victims or had connections with Ayrshire. Suzanne, family stories can get confused as they pass down through several generations, so it's worth considering whether your relative might have gone down with another ship. There were a great many such losses during the Great War just a few years later.