Therapy dogs aren't born
They are made from lots and lots and lots of training. I have one, we do hours of training a week and have done since she was 8 weeks old (she is now 3)
I think you mean 'calm lapdog that can be my DC's best friend' rather than therapy pet, unless you want the dog to do specific tasks?
This is an overview of what happens at a therapy dog assesment - to give you an idea of both the personality traits and training you will need to be looking for
"Walk on a relaxed lead, without excessive pulling and without the use of head collars, harnesses or check chains. Why? PAT dogs need to be under the owner’s control at all times, without relying on the use of training or behaviour correction aids.
Accept being stroked and handled and having their paws, tail and ears checked by the assessor. Why? PAT dogs have to accept being patted, often vigorously. They need to not be overly worried about having their paws, ears, or tail handled.
Take a food treat gently without snatching from the assessor. Why? Patients and clients love to be able to give their PAT dog a food treat. It is important that they do not snatch it because some patients, such as older people have very fragile skin.
Respond appropriately to a sudden noise or disturbance in the room whilst being tested. Why? PAT dogs have to encounter lots of new and unexpected stimuli – they should not be overly fearful of this and recover quickly"
You can really see why a dachshund is not going to be a suitable dog in many, many respects...
As I said in my earlier post, and another poster has pointed out, the list you've posted is very odd. The dogs have nothing in common other than being small and on the current designer dog list.
ALL dogs shed and ALL dogs can bring mud, ticks, water etc into the house. Their coat is a consideration for any dog owner, but should really not be the top consideration, especially when you've got a very specific ask of your future pet.