This question didn't have a tag for buying a pet; I've made an edit suggestion to add adoption. It seems relevant in this case, but adoption to me has the connotation of transferring ownership from one family to another, or perhaps adopting a rescue or a pet from a shelter.
Is there a better word we could use for buying pets from a young age, or is adoption suitable in all cases?
I think adoption is fine for all acquisitions, whether free, nominal cost (shelters), or purchases.
The issue of age is orthogonal; people both buy and otherwise adopt adult animals too, not just young ones.
There is no wiki for adoption, but personally, I wonder if adoption should be more about the adoption process and not actually bringing a new pet home.
Maybe a new tag for new pets regardless of how the arrive like new-pets
new-pets could be the synonym and adoption could be a tag
I think adoption is good for, well, adopting from a shelter or a rescue or from another family, etc, but if the pet is coming from a pet store or breeder, you could also consider purchasing, perhaps?
I know a lot of people, myself included, don't always like the connotation of a pet being bought - the idea of an animal you are going to consider a companion being something you buy just like you buy toilet paper or dish soap or what have you is kind of awkward.
That said, I think the actual word will come down to personal preference, but having both adoption and purchasing might not be a bad thing, I don't think, as they can have two different connotations in people's minds like I mention in my first paragraph.