Hi I also have 3 JRT's and they also foam at the mouth with the same frogs (I save them all day long during summer), they don't go to the vet because the frog pee is not toxic. Sometimes if the pee get's in their eyes they'll be irritated but again no need for a vet just rinse with cold water...
These frogs are garden frogs and will bring no harm to dogs. However the more frogs you have the more snakes in your garden if you want to detour the snakes you take a can with a rubber lid (poke holes in the lid to let the smell out) and put a mixture of cat litter and moth balls and few cans of that around the garden should work ***Note: do not let your dog eat either, can be toxic...good luck with the frog thingy...