Doris Lessing's decision to begin her story in the third person is an interesting one. The third person description allows the author—or rather, the voice of the story—to view her childhood from an almost anthropological perspective, describing the "strangeness" of it in vivid detail. Just as this child knew legends and stories about alien, "English" things, which did not allow her any understanding of the place in which she was actually growing up, the third person narrative turns this little girl into the subject of a story, too. By describing the girl, the veld, and the activities of the servants and the household on the farm in the third person, Lessing is able to think about them from a distance. This distancing enables her to think about how they would have struck another person, rather than how they seemed to a child who had grown up in this situation and therefore did not know anything else.
The shift into the first person occurs about two pages into the story. Its effect is, first, one of revelation: we realize that the speaker has been talking about herself all along. Another effect is that it suggests a slide into understanding. When the speaker was a little girl, she took everything around her for granted. When she turned fourteen, she began to see the world more clearly and perhaps be more analytical about it. While the speaker no longer recognizes the little girl as being the same person she now is, the moment she becomes "I" seems to be the moment at which she feels she started to be her current self.
The narrative doesn't shift back into the third person. One could argue that the final paragraph, taken out of context (which describes an imagined "settler"), is in the third person, but in context it seems to follow on from the paragraph preceding and represent a thought the "I" of the story has had.