At a minimum, both Roxy and the stud dog would need the following:
OFA hips and elbows-these x-rays can be taken by your vet and sent to OFA for evaluation. The purpose is to ensure that neither dog has hip or elbow dysplasia, which are inheritable problems. Ideally, great grandparents and grandparents of both Roxy and the stud dog would also have had this done. The problem with hip dysplasia is that it is often not obvious and you can't tell without xrays. Also, if ancestors of Roxy or the stud dog had hip dysplasia it is very possible that their puppies could have it as well, due to the unknown inheritance of hip dysplasia.
OFA for heart-this should be done by a veterinary cardiologist. They are checking primarily for SAS, which is a heart defect that can cause sudden death as a worst case, and can cause murmurs of varying degrees in other cases, with varying impact on the health of the dog.
CERF for eyes-Goldens have a number of inherited eye problems ranging from juvenile hereditary cataracts, which may not cause vision problems in your dog but, if bred to a dog with this in its background could, to pigmentary uvieitis, an increasing common problem causing pain and leading to eventual blindness if not caught and treated early. Dogs who have been bred need to have their eyes checked every year, as some of these problems don't show up until a dog is older.
Neither Roxy or the stud dog should suffer from allergies or thyroid issues, both being very common in Golden Retrievers.
The reason for these health checks is so that the puppies you are responsible for, are given the best chance in the world to be healthy and pain free. And to make sure that their families don't have to suffer the consequence of owning a dog with chronic health problems.
And it would be good to have Roxy and the stud dog evaluated by someone familiar with the Golden standard, ideally by someone who competes in conformation or field. A poorly constructed Golden can be subject to joint and bone problems later in life.
This is also not necessarily the best time to be having a litter of 8-12 puppies, who will have to be kept, socialised and exposed to different experience prior to going home at 8 weeks of age. You need to be prepared to hang onto to several puppies for the weeks or months it may take to sell them. Puppy buyers are increasingly more sophisticated and aware of what clearances are necessary, so not having them can put you at a definite disadvantage. And, you are not going to want to sell your puppies to just anybody with a checkbook or cash, so you may need to hold onto them until the right homes are found.
Not to mention the not-so-fun part of breeding. We have at least one breeder on here who lost her darling girl during the whelping process, and another one very recently who almost lost his girl. Both breeders incurred huge vet bills, and almost lost puppies as well, as they struggled to feed and care for new born pups whose mother was either dead or too ill to care for them.
Breeding is a huge responsibility and needs to be done the right way, not only for the sake of the puppies, but for the families they will join.
Please read this
http://www.grca.org/allabout/a_find.html
and make sure you would fit the requirements recommended to those looking for a Golden puppy.