samples for different objects with unique labels
Have run into this problem, when we wanted to run with patient-based deep learning models or individual observations (the same patient could have come several times) based deep learning models.

In your case, they could be analogous to Animal-based model vs general-one-for-all model which has all the animals. 

Pros of animal-based:


If you are going to build an animal-level classifier, it certainly is going to generalize better when compared to one-model for every animal.


Cons of animal-based:


If you don't have enough data for one particular animal, you can't help out much, for that case. This is slightly advantageous as well, I can't say for veterinarian examples, but if you are going to use a general-one-for-all model it might misclassify the prediction as well (because of lack of data for that particular example).


I would suggest you try both. There is nothing certain in this world. Only hunches and guesses from past experiences.

Hope this helps.