Think I would probably go by what the vet advised, purely because she is an obsessive egg layer. I put one in for my tiels in the hope that she would go into the nest box to lay her eggs. She isn't an obsessive egg layer though.
A picture of my teils and their hut, now it is only a small one as Leo (female and under the hut) was the only one who went in there, once she started laying her eggs (to the bottom of the cage

) Gemini also got in there with her, they didn't mind the squash it seems.

I have since got them a much larger one so they have plenty of room to get inside comfortably.
Is your tiel outside or inside? If inside then I wouldn't worry to much about her, she won't freeze and also even if you do put the hut in there, there's no guarantee that she will go inside it, Leo used to sit on the top of her one, it took her ages before she actually went inside. Now you can't get her out.
As for size, if you feel your Quaker would be happier in a larger one then get a larger one. Maybe as you've already got this one, it might be an idea to let your Quaker try it first, again he may have no interest in going inside, and if you buy another one and he doesn't like it its money that could be used for toys etc.
When do you get your New family member? Hope we get to see some pics.