If I want to ask the question about the dog, whose name is
Cerberus should I ask
Quis est Cerberus?
Quid est Cerberus?
Do we use
quae (according to gender) about animals or
What is the rule here?
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Quis and quid are both grammatical here, but mean different things.
"Quid" is a pronoun meaning "what", and can be used that way even in a sentence with a masculine, feminine or plural subject:
Ipsi enim quid sumus aut quam diu haec curaturi sumus?
(Cicero, Epistulae ad Atticum 22.214.171.124)
Quid est enim exsul?
(Cicero, De Domo Sua 72.3)
So if you mean to ask "What is Cerberus?"/"Cerberus is what?", you can say "Quid est Cerberus?"
"Quis" means "who", so if you mean to ask "Who is Cerberus?", you can say "Quis est Cerberus".
Compare English: "What is Cerberus" and "Who is Cerberus" are both valid sentences; they just mean different things.
Of course, Latin is not English. But similarly, compare the use in Latin of id vs. is: I believe id est Cerberus and is est Cerberus are both grammatically valid. Since a demonstrative pronoun like is/id does not have to agree with the gender of the other noun in copular construction, I don't think the interrogative pronoun quis/quid has to agree in this construction either.
In terms of grammatical resources, here are some reddit posts I found:
Also the questions listed in this handout "Developing oral skills in Latin", from the website of the New York State Education Department, show usage of quid vs. quis according to the meaning of the pronoun, not in agreement with the other noun in the sentence:
Ask the following questions
Teacher: Quid est Campus Martius?
Student: est locus
Teacher: Nunc quid est Spartacus?
Other alternative interrogative pronouns: