It depends on how ready your kid is. You can probably tell. :) Usually, kids as young as 6 or 7 years old can already take on the responsibility of caring for a pet. Just be sure to guide them. Stumbled upon this cute article you might enjoy: https://ph.theasianparent.com/26-photos-prove-kids-need-pet/
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IMO, 6 Years old! It's better to expose kids to responsibility, as a training ground. But still, we should educate our kids to know the responsibilities of taking care of one.
My kids had a pet since day 1. he is 3 years old now and he feeds his cat every morning before he goes to school and in the evening when he returns from school.