For a fairly wealthy family in the 19th century. I know the job of a nanny is hard when it involves changing diapers. And from what I gather the nanny was also the child's first teacher. But as the child got more independent did the work of the nanny change to take on other estate duties? Assuming that there wasn't an endless stream of younger siblings to take care of. How long would a nanny expect to work for one family at a time?
A woman who was a nanny would continue in that line of work, rather than being given duties in the kitchen or something after the child was grown.
Upper- and upper-middle-class infants were typically put in the care of a nursemaid, a position which became known as a "nanny" by the end of the century. (Isabella Beeton estimated that a family with at least £300 a year could and should hire one, along with a maid-of-all-work; it's only above that level that cooks, housemaids, etc. were suggested. That should tell you how difficult and time-consuming taking care of an infant is even outside of diapering!) The most affluent establishments would have an "upper nursemaid" or "head nurse" in charge of the entire nursery, with lower nursemaids under her direction. If a wet nurse was being used, as she very well may have been throughout most of the nineteenth century, she would be below this upper nursemaid in rank, although the wet nurse sort of existed outside the nursery structure - her job was to provide a commodity, milk, rather than to look after the child itself, unless said child was being placed in the nurse's home.
Nursemaids would feed babies, wash them, dress them, take care of their clothes and toys, take them for walks, teach them good habits, and report on their condition and progress to their parents. When there were lower nursemaids, they would do a lot of messy work around the nursery - scrubbing the floors, bringing up and taking away meals, lighting fires, making the beds - possibly in conjunction with a "nursery girl" who would do the worst of it. The upper nursemaid, or the only nursemaid in a smaller household, would have to know what to do for teething, colic, croup, and other childhood ailments. She would also have to be someone with good references as to her character; in the best cases, she would be clean, sober, and careful, but some certainly were abusive. The future Viceroy of India, once grown, would describe his and his siblings' nanny as having kept them in such a state of terror that they were too frightened to tell their parents of the beatings and painful punishments she meted out.
Some nursemaids stayed with a family through successive generations of children - possibly going to another branch of the family while the ones they raised grew to maturity? - but most would leave the household once their charges were in the care of a tutor or governess and find employment elsewhere, either by answering an advertisement in the newspaper, signing up with an agency, or just going through word of mouth.