The only note of concern is that my daughter who is almost 12 is extremely nervous around dogs.
Have you already mentioned this to the breeder? If not I'd do so now as it's pretty normal for a breeder to want to see how family members act around their adult dogs before introducing them to the puppies. If you let them know beforehand they can, if necessary, modify how they do introductions with the adult dogs.
The breeder may be reticent if your DD is very scared and not unreasonably so. All puppies are bitey, jumpy little things and labs particularly so.
Health test wise, as an absolute minimum both parents should have had:
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their hips scored with results at least lower than the current breed average (currently 10.8 I believe) but preferably as close to 0 as possible
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their elbows scored with results of 0 (and certainly not higher than 1)
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a clear eye test under the BVA scheme within the last year
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DNA tests (with at least one parent testing clear) for prcd-PRA, Centronuclear Myopathy and Exercise Induced Collapse
Ideally they should also be having the litter screened under the BVA eye scheme plus DNA testing the parents for Achromatopsia, Leukodystrophy, Congenital Myasthenic Syndrome, Cystinuria, Degenerative Myelopathy, Skeletal Dysplasia 2, Hereditary Nasal Parakeratosis, Macrothrombocytopenia, Narcolepsy, Retinal Dysplasia and X-linked Myotubular Myopathy.
It's acceptable to skip DNA tests on a dog when they have parents who were both DNA tested clear for that particular condition as this means the dog can't be anything but clear.
It's also worth asking about the coefficient of inbreeding for the litter. As KC breeds have closed studbooks there's a very finite amount of genetic diversity within each breed. Good breeders should be doing everything they can to maintain this diversity by considering COIs when breeding and aiming to produce dogs with a lower COI than the breed average. This article explains really well why this is so important. The current official average COI for labs is 6.5%, the litter's COI should be below this and preferable as close to 0% as possible.
If you have the full names of the parents you can check for the results of certain health tests (hips, elbows and eyes plus the DNA tests for prcd-PRA, CNM, EIC, SD2 and HNPK) and the COI of the litter using the KC's Mate Select service.