I was told I needed to get my mini dachshund x-rayed before I breed her. My husband and I are keeping all of the puppies ourselves since we cannot have children.

You will need to get her more than x-rayed.
Yes x-rays will help determine the condition of her spine as dachshunds are prone to back problems.
You will also need to get full bloodwork done on her and dna testing for genetic problems.
This will also need to be done to the sire of the puppies.
It is recommended that both parents and grandparents have their AKC championship title and they are of excellent quality.
Breeding should only be done to better the breed and to pass the sire and dams good qualities to the next generation.

If you are considering breeding you will need to find a breed mentor and have witness several litters being born to help you better understand the process.
To be honest, reading about breeding dogs does not mean a lot, it's all down to experience, however I would highly suggest you take a look at this website...

Breeding Responsibly - Finding a responsible breeder - Bringing up puppy (http://www.woodhavenlabs.com/breeding.html)

They have excellent information about breeding, why it should be done and why it should not be done.

Where are you from?
If you provide a rough location I bet quite a few members on here could find dozens of dachshunds in shelters that would love to find a forever home.
There have been many, many questions about dachshund breeding on this site over the past few months.

Just to reiterate Shaz, both of your dogs should be champion dogs with titles, have health testing done (knees, eyes, etc etc) before you even consider breeding.
There are far too many dachshunds dying in shelters every day for someone to breed more.

I would also like to add that you need to be aware that breeding your dog does impose a certain level of risk to the mother. Seeing as how cannot have children I'm sure that losing your dog due to complications would probably be beyond heartbreaking for you and your husband as well as tragic.