I think there will be three points to consider here. The first being the emotional strain on a child of that age obviously upset at the death of his grandmother to face such public scrutiny. Secondly, particularly after (in my opinion) the extremely intrusive photography of the two royal vigils at Westminster Hall, when his every expression will be captured, and later commented on, perish the thought that he might screw his face up or yawn. Thirdly the logistics of processions, seating etc.
I have been at many funerals when children of that age have been present with no problems, but in this case I would say No.