Why is it not good for a to get pregnant the first time she goes on heat? (She's a miniature dachshund, between 7 - 8 months old and is on heat for the first time.)

Not good because she isn't completely mature yet. And its 'in heat', not 'on heat'. Get her spayed, as is appropriate for a pet. Then you won't have to worry about unwanted pups, and possibly a mixed breed.

Tick

Because you're dog is still very immature and still needs to grow. If you breed her now, those pups are going to steal a lot of things from her that she needs right now.

Is it OK for a 16 year old girl to get pregnant?

Same thing.

You shouldn't even be worried about when you can or can't breed her. The world has enough dogs.. You don't need to add to it.

Besides.. If you WANT to breed. You should prove your dog. Meaning.. Enter the show world. There are many things that AKC offers to put a title on your dog besides the breed ring.

And remember.. not every dog that is AKC registered is worthy enough to breed. And that's OK! You dog may make a great pet. The old wives tail of having to breed your dog to "settle them down" is a complete myth. Breeding your female may cause a huge mood swing that doesn't leave. She will definitely lose her puppy-like behavior. Spaying her will ensure that she doesn't make those changes.

Also.. a good breeder won't breed on the first or even the second cycle. They typically wait until the 4th or 5th heat cycle.

Please read up and educate yourself if you wish to breed your dog. It is a lot of hard work. If you breed, make sure those pups go to good homes. You may want to even consider sending those pups out on limited registration - meaning, your pups will be spayed or neutered before the AKC papers will be sent to the new owners. It will ensure that no more dogs will be put on the ground.