I'm on the fence about this. I think for primary school, it's just not a good idea, full stop. The limited benefits of having a dog as a 'therapy animal' in a primary school are outweighed by: the distraction for young children, the fact that primary schools are extremely busy noisy environments, the fact that many very young children will not be able to articulate if they're scared of dogs, and many young children aren't able to exercise self-control and leave an animal alone.
At secondary school, I think a therapy dog can often be a good thing. I should be clear - I'm saying 'therapy dog' because that's invariably how it'll be presented to parents, but essentially it's a teacher's personal pet, brought in on the understanding that children who need some regulation can spend time with it. Don't ask me how they sign off on the H&S of this!
At my son's secondary school, there have been dogs belonging to the librarian who always stay in the library. (one dog at a time, over a long timeframe) Kids who needed a bit of calm time or comfort are able to chill with the dog. I sometimes asked DS, did nobody object because of fear of dogs, allergies etc? He said he thought not. At another local school, there was a dog brought in by an art teacher that was based in a pen in the art block but was taken on supervised walks around the school as therapy.
Both these examples seem to have worked out at these schools and helped students regulate and feel happier.
I think a dachshund in a primary school is asking for trouble though! They tend to be really barky and excitable. I live next door to one and the bloody thing never stops having hysterics.
(at the back of my mind, I can't help thinking this is basically a way for a dog-obsessed staff member to bring his or her pet in with them every day. And I'm not convinced that personal pets belong in the workplace.)