"Taking animal nourishment" is simply a wordy way of saying "eating".
While in some contexts "animal nourishment" might mean "meat", in this context it probably means food in general -- there is no context in the text to suggest that any specific kind of food is intended. Indeed, the description of the boy as "corpulent" (i.e, obese) earlier in the text suggests that he may have occupied a considerable amount of his time in "taking animal nourishment"!
The adjective "animal" might have been used here to contrast "animal nourishment" with "spiritual nourishment", e.g. religious study or education, neither of which the boy seems likely to have engaged in. Alternatively, it may simply be an unusual circumlocution -- Dickens is known for his wordy and sometimes excessively elaborate writing style.