I think you're making the mistake of over organizing things.
In the actual GTD book and most setups of people associated with it, the only solid connection between specific actions and 'projects' is you. It's tempting to want to have everything conceptually tied together and pretty in an overarching structure within any system you're using, but in the case of buying a dog-
If there are subtasks of the parent task of 'buy a dog' you hadn't considered but need to do in order to get your canine, just adding them in as subtasks of that parent task on the spot seems like it'd suffice. As long as you know where they are, will see them when you can do them, and most importantly you do them in order to get a dog, then the system works fine.
If you were merging companies and had a few projects as tasks in disguise like 'assess the people at the new company we acquired,' things that'll play out over the course of many weeks, months, or even years, you'd wanna consider breaking them up a bit. But not buying a dog. Unless you're looking to use that dog to win some Olympic dog contest in a really complex and elaborate life plan you've made, just list it as 'do x, do y, do z, get dog' ;).
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