While grasscarp (white amur) are a great biological control for several species of submerged aquatic vegetation, coontail is way down on their list of desirable table-fare. Consequently, they rarely do a great job of controlling coontail unless they're stocked at a fairly high density. Also, despite the quote that RAH posted, I've encountered many ponds where grass carp contributed to a turbidity issue; presumably when they overgraze the available plant life, and then either they (grass carp) or some other fish species (catfish?) seem to keep the bottom sediments churned up - creating a muddy-pond environment.
Regarding the dogs' consumption of treated water: I know of no aquatic herbicides that (once applied) pose an adverse threat to your dogs - or livestock/wildlife. Diquat is the only aquatic product that lists a livestock-consumption restriction, which only lasts 1 to 3 days post-treatment (depending on the use-rate). Endothal or fluridone probably offer the best treatment options for coontail, and neither one has a livestock watering restriction.
For what it's worth, the term "toxic chemical" is far more applicable to certain ornamental plants that dogs may encounter than it is to the limited number of EPA-registered aquatic herbicides.