Is vet a noun

Yes, the Word 'vet' is a noun, a singular, common noun; a short form for the noun veterinarian, a Word for a Doctor Who treats animals; an informal term for a military veteran; a Word for a person.

The Word 'vet' is also a verb, meaning to subject someone or something to thorough examination or evaluation to determine suitability, authenticity, or if it's allowable.