Will Jack Russell's kill?

Recently I had an unfortunate thing happen surrounding my Jack Russell, who is 8 months old. I take her to a small dog park where dogs are free to run with other small dogs. On this one occassion my JR, seemingly went up to another much smaller dog than she. The smaller dog turned and made the motion to nip my JR at which point my JR grabbed the smaller dog by the the back of the smaller dogs neck. The owner of the smaller dog picked up her dog. My JR held fast onto the smaller dogs neck. Two days later the smaller dog developed a blood clot and died. Is this typical behavior for a Jack Russell? Mr JR lives with three people so she is rarely alone. At home she is docile and playful. She can play a bit rough at times but we are firm with her as all the people in the house are men. Other times when I have taken her to the dog park she plays with the other dogs and chases them around. Her activities at the dog park always seem to be playful never aggressive, except for this one time. Should I take her to the dog park with other dogs that may be smaller than she? What do you recommend?