Using 'just' is good, but 'only' or nothing are also fine. We tend to avoid repeating a word, which is why 'just' is better than using 'only' a second time. 'Kid' is informal, and children tend to use informal words, so a child is perhaps more likely to say 'kid'. But both are fine.

In this context the 2 words, "only" and "just" are interchangeable. In terms of conversation a child is more likely to use the word "kid" especially when talking to other people of the same age group. Even adults tend towards the use of "kid" over "child" in every day speech but use "child" in formal situations. I don't know if you want feedback for this part, but in the same spirit of my last point, the word "pupil" is one that does not get used often any more in reference to students. The word "student" would be used instead but, also, the entire wording of the question feels formal which is not the way friends talk to each other. In English speaking countries you're more likely to ask "Does your brother go to school?". It's not directly asking if he is a student but it is implied within the question because students go to school.

[AmE]I would add that the question "Is your brother a pupil" isn't something that a kid would ever say. And an adult might say it, but it in a different context. A kid would say "Is your brother in school?" or "Is your brother in school yet?" An adult could ask something like "Is your brother a pupil at the new High School?" but would probably be more likely to say "Does your brother go to the new High School?" "Pupil" isn't usually used alone. I am a pupil of a famous language teacher. I am a pupil at the conservatory.

in my personal opinion I would say just, sounds much more cooler and nice I would use he is just a child* instead of kid to make it sounds cooler. I am just giving up my personal opinion