Thanks for your responses. I think they confirm my suspicions that this has Bad Idea written all over it, quite apart from the weak evidence on allergies.
She apparently grew up with puppies but this was on a family farm that she stayed at a lot with her grandparents. Sounds like a different ball game to me. I bet old-school farm puppies live mostly outside and largely toilet train themselves, and don't get a lot of vet care.
She works from home so the dog would have plenty of company, but I can't imagine her son actually being consistent about looking after the dog (he's not terrible, but he is a kid!), so the walking, poo, pee, chewing, cleaning up hair/dander/slobber, vet visits will just be another thing she has to deal with.
And she goes overseas about once a year (we are both foreigners in this country, so this is kind of "essential" and is what she saves any surplus income she can spare for), so yeah, what is she going to do with the dog then? I hope she does not think I am taking it, I am a cat owner and my cat hates dogs! Even if one of her friends is OK with taking a dog for 3 weeks, just sorting it out is going to be a source of extra pressure.
Expense, yup, I hear you.
And the pet shop industry in this country is not nice.
I think next time I see her I will make a strong case for trying a couple of mice or gerbils (if her son is keen on the idea), and seeing if her son is actually capable of fully taking care of them for at least two years without help, nagging or reminders. (He won't be able to meet that kind of bar, obviously, and hopefully once she has been through the 25,000th round of nagging and then resentfully cleaned out the poopy cage litter for the millionth time, she will be thoroughly disillusioned with the idea of a dog....)