But Dr Zungu, now 30, looks back with nostalgia to the days when these were her only worries. Last March she became the first woman in recorded history to be appointed a Zulu tribal chief. She now lives on a hill-top in the 'bundus', as she puts it, ruling the 70,000-strong Zungu clan.
'When my mother comes to visit me from Durban she just stands there staring, absolutely amazed,' she says. 'She knows nothing about all these tribal things. And then she comes here and we go to the supermarket in town and - I must say it's rather embarrassing - half the people we see come up to me and bow.'
As if to prove the point, half-way though our interview a man in his twenties entered the room. A picture of servility, hunched, hands clasped, he took two steps forward, went down on one knee and, head bowed, staring at the floor, informed her that an officer of a South African Defence Force platoon was waiting to see her. He must wait, she ordered, until the interview was over.
Quiet authority, clearly, comes naturally to her. But in other departments she has had her awkward moments. 'You must understand that because of the kind of family I had - my father was a schoolteacher - I was brought up knowing nothing at all about tribal customs.'
As a result she has put her foot in it on more than one occasion. 'We were at a party with a whole lot of other chiefs where they slaughtered an ox. Now, according to the culture, I later discovered, women don't eat the parts of the head.
'So I was sitting there with the chiefs, and they brought along a tray for us with choice bits to eat - tongue and brains, mainly. I wanted tongue, and so there I was busy eating a piece, when one of the chiefs, totally shocked, said to me that women aren't supposed to eat that.
'It was all terribly uncomfortable, but luckily another chief broke in and said, 'Yes, that's right. But chiefs do, so go ahead.' ' (An expert on Zulu customs later explained that women were not allowed to eat tongue because they talked too much and should not be encouraged.)
Dr Zungu experienced similar discomfort at a grand Zulu ceremony at which a number of 'the royals' were present. 'Not the Zulu king himself, but close relatives, princes. Now, to begin with, everybody turned up in traditional attire: leopard skins and that sort of thing. I was dressed in a modern, fashionable dress. Also I got the protocol all wrong. Chiefs are supposed to lead their people down the road, singing and dancing, then greet all the other chiefs before taking their seats. I just drove up in my car, got out and strolled up to the place reserved for me.'
She acceded to the chieftaincy after her husband, whose line of chieftainly descent went back 160 years, died in a car accident. Quite why, or how, she was appointed would always remain a mystery to her, she said, because other blood relatives of her husband, some of them male, seemed to have at least as strong a claim.
'Quite out of the blue one day I received a letter from the KwaZulu government informing me that I was the chief. I have no idea to this day why they chose me.'
Possibly the main criterion was that her husband had worked as a deputy minister in the KwaZulu government and was thus automatically a member of Mangosuthu Buthelezi's Inkatha Freedom Party, which exercises one-party rule in the homeland.
'I myself belong to no party. A chief should treat everyone equally, independent of their politics. I have my beliefs, of course, but I keep them strictly to myself,' she said.
Her conversation leaves little doubt, however, that her sympathies lie more with the Inkatha conservatives than with the African National Congress, fierce rivals in a Zululand civil war from whose consequences the Zungu clan has not been immune.
Unfashionably, for someone of her 'Western' background, she thinks blacks are not sufficiently well educated at present either to run the country or to hold elections. 'Democracy is all very well, but we should delay it. The thing about elections is that they will definitely bring more violence. People are not prepared to be good losers, like the whites have been in their elections.'
Her fears are founded on the fact that nowhere in South Africa has the ANC-Inkatha conflict been more acute than in the Zululand area this past year. Since she became chief, more than 40 of her clan members have died. She is not taking any chances. Amid constant rumours that her life is under threat, she does not travel anywhere without an armed bodyguard. 'It's not nice - but what's to be done?'
She has thought about resigning the chieftainship, but says she can't. She knows there is no one in the clan better equipped than she is to take on the responsibilities. These include analysing the community's problems - mainly the limited water supply, 40 per cent unemployment, poor education and, of course, violence, criminal as well as political - and advising the people how best to cope.
But there is more to it than that. She has a bureaucracy to run. The KwaZulu government provides her with funds that she has to administer and distribute. She is also the Zungu clan's chief justice. She runs the tribal court, an institution which does not deal with serious crime but addresses endless land disputes, stock-thefts and the like.
'Look at this case I'm sitting on now. A man has two wives, the first of whom bore two children by another man before they married. The first wife died recently and he's decided to dismantle his home - literally pull it down - and move in with his second wife. Now, the second wife is on bad terms with the two children, who are both teenagers now, and she will not have them in her house. So, the question is, where are they to live? It's terrible. I alone have to decide what's to become of these people's lives.
'Sometimes I just look at my husband,' she said, turning to a wedding picture on the wall. 'If he was here now, I'd tell him to stay in this house while I disappeared. But I can't. My main problem is that I've been landed with this, and if I leave it I'll be dishonouring my husband, and I'll feel guilty for the rest of my life.'