Hello, my name is***** and I have over 20 years of experience as a veterinarian. I am sorry to hear that Hobson isn't feeling well. Nitrates themselves aren't toxic but they are converted in the body to nitrites, which are toxic.
The short answer is yes, if they are at levels that are dangerous for babies they could be dangerous for your puppy too.
If the amount of nitrates in the water is such that it exceeds the capacity of bacteria in the intestinal tract to form ammonia, nitrates and nitrites can accumulate and be absorbed into the blood.
Signs of toxicity occur when hemoglobin (the oxygen carrying part of the red blood cell) is converted to methemoglobin because of the effects of nitrite. Once methemoglobin concentrations reach 40 percent we see obvious signs of illness. Signs include weakness, blue or muddy colored mucous membranes (gums), incoordination, and collapse. Blood can appear chocolate brown in color. When methemoglobin concentrations reach 70-80 percent, death can occur. Nitrate poisoning can also cause abortions.
In your pup's case it may be that her levels of methemoglobin haven't gotten high enough to cause changes in blood or mucous membrane color.
It would be worth mentioning your concerns to her veterinarian and checking blood nitrate levels.
In the meantime after her blood is taken I would only give her bottled water to drink.
Please let me know if you have any further questions.