https://filestore.aqa.org.uk/sample-papers-and-mark-schemes/2018/june/AQA-77021-QP-JUN18.PDF
The quote essentially makes the stance that the pragmatics of a child's language is the "best" thing to track to explain its development. The question is encouraging the student to talk about other major aspects of language: phonology, syntax (grammar), lexis and semantics, and morphology. They can also talk briefly about prosody, because the data set includes Child Directed Speech (CDS) and emphatic stress, though this is limited because the data cannot be heard. The best strategy to cover a lot of ground is to dedicate a paragraph to: 1) pragmatic development, 2) phonological development, 3) lexical and/or semantic development, 4) grammatical development, and then end each paragraph by relating it back to the question, to essentially say "this non-pragmatic phenomenon is also worth watching because it reveals a lot about the child's language development in the ways that I have described".
For pragmatic development, students should cite David Crystal (1986) 'The Cambridge Encyclopedia of the English Language', which details the evolution of children's "protoconversations" into more meaningful conversations over the period when the child is between 2 and 4 years old. They would relate this to the data as is necessary. Students may also cite Michael Halliday (1975)'s 7 Functions of Early Child Language (instrumental, regulatory, interactional, heuristic, personal, imaginative, informative/representational), and may discuss a few of these relative to the data to show off more general knowledge of child pragmatics. For phonological development, the student may discuss Crystal (1986)'s pre-verbal stages and show how these can indicate the stage of a child's pre-verbal language development with relative precision. There isn't much interesting lexical/semantic stuff to talk about in the data but students can discuss things like overextensions and diminutive forms and talk about how the more accurate a child's use of words for the correct meaning indicates development. There is a lot of interesting syntax in the data, so it would be worth discussing stages of grammatical development, e.g. citing Bellugi and McNeill's stages of interrogative and negative formation, and Roger Brown's U-Shaped Regression Model, which also indicates the stage of a child's language development. After all these paragraphs, the student should end by weighing up the value of each set of evidence versus the evidence that pragmatics is the best way to explain children's language development. Following these guidelines, they should have a technically impressive, skilfully written, easy-to-read weigh-up of which branch of linguistics is most indicative of child language development. As these all develop at the same time, with some aspects drastically speeding up at certain points in a child's language development, it would be most reasonable to say that all branches of linguistics are arguably the "best way to explain children's language development".