I have a 15-week-old puppy. My baby is a purebred dachshund. She sleeps an awful lot. We'll take her for a walk (20-40 minutes), she will play for about 10 minutes, and then she is out like a light for 3 to 4 hours. Is this normal or is my baby a narcoleptic?
Yes, this is absolutely normal; no, your baby isn't narcoleptic. Puppies sleep a lot -- just like babies and toddlers. If you take a look at this source, the estimated amount of sleep that a 16-week-old puppy should get is 18-20 hours/day. Gathering from my own personal experience and various sources across the web, I'd say the number is closer to 15-19 hours/day, but regardless, if your dog is up and about for a few hours, she's doing just fine.
Additionally, dogs are considered to be "crepuscular" mammals, which means they're naturally most active during twilight hours (see the diagram below). So if it's been a few hours since she's woken up in the morning, it's 100% natural for her to take a long nap. Again, the naps will be exaggerated because she's still got growing to do. If your dog were narcoleptic, you'd see more obvious signs.
If you're still truly worried about your dogs sleeping habits, a trip to the vet may be the best way to deal with it. However, from what you've said, your dog's behavior seems to be consistent with that of a 15-week-old puppy and you have nothing to worry about. For now, take advantage of it.