I took the cat to the vet
If you went by a car - я вёз кошку к ветеринару If you mean a complete action, then: я отвёз кошку к ветеринару.
If you walked without a car - я (от)нёс кошку к ветеринару
If you say just 'I took the cat to the vet' - this is correct variant: Я взял кошку к ветеринару. Full version: Я взял кошку, чтобы отвести (without or by a car)/отвезти (only by a car) к ветеринару. But it is analog of PRESENT perfect of English.
If you wanna say in the past, this will be: Я относил/носил/отвозил кошку к ветеринару.
Отвозил = by car
Относил/носил - by walking