Owning a pet is great fun, a great learning opportunity and, as you apparently realize, a great responsibility. When children are very young, safety for both kids and pet is a primary concern.
Young children move fast and act impulsively.
Without any bad intentions they can be rough with a pet, which can lead to harm. Beyond safety concerns, the big issue is responsibility. I'd suggest you look closely at how well your children currently follow directions and carry out their household chores from day to day without reminders. Or you might want to start with a pet that requires less care than a cat or dog, letting your children work their way up to a greater level of responsibility. Once you decide that your children are mature enough to own a pet, I'd suggest a family meeting to come to agreement about how you all will care for and train the pet.