I don't think anyone here is going to agree with impuse buying. 99% Are not going to agree with any sort of "buying".
An impulse buy is not buying everything you need and doing your research to take care of the pet properly. Often it means picking the cheapest cage set up at the store, crappy food, or even just the pet and throwing it into a rubbermaid container when you get home!
So, with an impulse buy, you have an animal in your arms, that you don't know how to take care of, have no idea how long it will live for (5-7 years for guinea pigs and rabbits is not uncommon) don't have a proper set up for, and have not really given serious though to how much time you will have for the pet, or how you will feel about cleaning out poo from the cage 6 months / a year down the road.
With a child involved, it is even worse, because the animal is usually treated as a new toy, as what happens to almost all toys, once they are no longer new they get ignored for the new shiney ones, leaving a pig sitting in a cage overdue for a cleaning, often not being fed regularly, lonely, (because the impulse purchaser rarely purchases two or more) and with the next big clean up on moms part, or next family vacation that is planned, the pig is boxed up and dumped at the local shelter!
Yup, impulse shopping sucks! Especially when kids are involved. The animals almost always end up dead from improper care, or at the very least, neglected and dumped!