. I found the breeder on pets4homes however I have just checked and they are not KC registered.
No! Dachshunds are 'popular' at the moment ... a lot of the supply for the increased demand MUST be coming from puppy farms and dodgy foreign imports.

We have a 12 year old standard dachshund, we adore the breed - so obviously we talk to other people with dachshunds when we're out, and quite a lot don't look like they're the real deal - clearly not from proper breeders. So who knows what health issues they may have. You could be landing yourself with a world of grief and vets bills.
Even if you had found one from a reputable breeder, I'd still be saying no. Some dachshunds get on with other dogs, some don't. A puppy of any sort sounds like it would add to stress. Dachshunds aren't 'yappy' - they bark, best value bark per pound of dog going. And I honestly can't see how having a new dog taking your attention is going to help your DD at all. Dachshunds are a breed liable to fixate on one member of the family - mine pines for me if I'm out.
I'm glad you posted and asked here, hopefully you'll take the advice on board. I hope you find some other ways to help your DD.
And at the point your current dog dies - hopefully not any time soon! - if you still want a dachshund, do your research, take the time to find a proper breeder (when our last one died we'd have had to wait at least six months for a puppy from a breeder we trusted, we were very lucky to find a 10 month old sooner)