I have a tiny female Yorkie and I have spent zero on her Vet bills.
I suggest you take your time and find reputable breeders first. Do not rush into this and settle for something you don't want. While it is very difficult to find a smaller female, finding one that will be 5lbs. shouldn't be that hard. For a young person (who's back is still in good shape
) that might be a good size. She won't be quite as fragile but she will still be small enough to include in your adventures.
It may not be impossible to find a smaller female under 4lbs. for less than $1000. but it will be very difficult.
Take your time and make finding the good breeder with healthy pups your main priority...then wait for the right pup.