Heather, you have to wait until 2 for the hip and elbow clearances, but you can do the heart, eyes, patellas, and thyroid after one year of age. And you can send away for the cystinuria DNA test at any time then send the result in to OFA for a clearance....even at 10 weeks of age.
(The dogs aren't AKC tested...they're OFA cleared, or not. OFA is the Orthopedic Foundation for Animals which maintains a database of dogs and their submitted health information. A CHIC designated dog has been tested for all genetic diseases specified by the breed parent club (and sometimes more than those recommended). In this case, the parent club is the NCA. Just because they're CHIC dogs doesn't mean they PASSED the tests...just that they were tested and the tests were made public on the OFA database. Various Vets do the testing. Opthamologists for the eyes, Cardiologists (not always but if you can, get it done by a Cardio Vet) for the heart, a DNA lab for the cystinuria test, your Vet can do the xrays for the hips/elbows...which are then sent in and reviewed by a panel of 3 Orthopedic Vets at OFA to determine their "grade". Your Vet can also check the thyroid by sending the blood to a lab, and the patellas. Each of these tests has a specific form that needs to be filled out and signed by the Vet doing the exam. Those forms are all on the OFA website so you can print them out and take them to the vet, after filling out your part. Once the tests are done, and the paperwork filled out properly and signed, you can submit them to OFA for the database). Here's the OFA link. To find a dogs/bitches results, you'll need it's full registered name:
www.offa.org Not everyone submits results to OFA...even passing results. However, to find out how a dog/bitch "looks" genetically (as far as those specific tests go), OFA is the best place to look (at least first). You do want to see the results of all of those tests when deciding upon a stud.
You also need someone to evaluate your girl for conformation (to see if she meets the breed standard), which should be done by a show breeder, and if it looks promising, get her into some shows to see how she does. And then, be mentored by someone (perhaps your own breeder, or perhaps someone else) who can go over the pedigrees to look for the strengths (and/or weaknesses) of any potential stud for her. Go to some of the top Newf breeders websites and take a GOOD look at their dogs. Look at the pedigrees, and hunt (Google helps) for photos of the dogs in them. Pretty generally, you'll see uniformity in the lines. The breeders are working towards a goal. They want a certain head, bone, straight topline, gait, front, rear, tail set, ear set, eye set, etc. It takes MANY years of careful breeding, knowing lines and health issues, to get the result they're looking for. That's the kind of mentor you should have.
Here's a link to the breed standard, with illustrations of what you do and don't want ... just keep scrolling through to see all parts of the body:
http://www.ncanewfs.org/publications/illustratedguide/illusguidecontents.html
And this is the written NCA breed standard:
http://www.ncanewfs.org/standard.shtml
Genetics are important for more than just health. They also determine everything about the dog, including temperament, structure, coat, working ability, bone density, etc.
Before you get into breeding, you'll need to start doing a lot of research, and have a lot of discussions with someone who can head you in the right direction.
The lady in NY who breeds browns is Helen Mancuso. Niki Hardin (newfiemomof2) here on NN can possibly help you get in touch with her if that's what you'd like to do. Perhaps by having a conversation with her will help you start figuring out the lineage of your girl, and where you might want to look for a potential stud if you decide that she should be bred at all.
Remember, the purpose of breeding should be to improve the breed. To do that, there are SO many things to take into consideration before taking the plunge.