She made the dog from scratch. It's not a modified creature, it's an artificial lifeform she created. Augments/Genetic Manipulation is only illegal on citizens, not animals or artificial creatures.
Lots of Federation species engage in augmentation, Denobulans for example are extensively augmented. Its just humans that think it will inevitably turn them into monsters, sort of like Vulcans and emotions.
What about Starfleet’s behavior towards the Illyrians, though? It suggests that the law affects all species in the Federation, rather than it being some sort of United Earth law.
We know that there was a Starfleet regulation preventing their service without special dispensation. As far as discrimination, its probably that they looked too much like humans. The Federation isnt quite as enlightened as they like to think when it comes to their own prejudices and bigotry, as shown by the likes of Data and the Dr.