You asked when she would "have to" go to nursery and school. She doesn't have to go at all.
You can start her at a day nursery as early as you like if you are prepared to pay and can find one which suits. They provide childcare for working parents but can also take children whose parents want them to go for other reasons. She becomes eligible for the government funding in the term after her third birthday, but you can send her later if you prefer. Some children don't go to nursery/preschool at all.
If you were thinking of private schools then they take children from various ages, so it would be worth finding a school you like and asking them what the options are.
Your dd becomes eligible for state school the autumn after her fourth birthday, so the earliest she could start is autumn 2016 at about the time of her fifth birthday. If you don't want her to start then, you can defer her start until she reaches compulsory education age in the following term (Jan 2017) without risk of losing her place.
Or if you would rather wait longer, you would need to home educate from the time she reaches compulsory education age in January 2017. It's straightforward to do and you can choose any approach which suits your daughter including learning through undirected play. Then you can start her at school whenever you want. The Local Authority is obliged to provide a school place for her when you ask for one. However, starting later than January 2017 might affect her chances of getting a place at an oversubscribed school of your choice. So if you feel strongly about which school she goes to and if it is likely to be full, then you could consider having her start by that time.