You're way too nice...
I have to jump into this thread; I was hesitant since I'm still fairly new to the forum, but.....
WHY are you giving this person the time of day? Unless she is physically blocking your path, I don't get why there is even a conversation? Her questions are - to me - intrusive, judgmental and serve no purpose at all other than to rile you.
My little sheltie is still quarantined to my home until he finishes his last round of shots, but I have an almost 8-month old Shiloh that I take everywhere with me so he can get used to being around different people and different environments. He's a plush black sable, and already 80+ pounds, so I get a lot of questions. Most are innocent (omg, he's so fluffy! Is he a (fill in anything from German Shepherd to Malamute to Malinois) mix); others intrusive (how much did you pay for him? I've got a (fill in the blank) female; we could breed them!) to the judgmental (y'all need to put a muzzle on him he could bite!<this from a man who tried repeatedly to pet my dog even after I lost my cool and told him to 'keep the %$^% away from my dog' and my dog (puppy, actually), raised his lips, most likely in fear).
It seem that no matter what, this woman has an answer that ticks you off after she asks you a question (agility? Why? are you planning on being on TV? Your dog's not a showdog, why are you PUNISHING your dog?...

) I get that she's your neighbor, so you have to play nice, but maybe she'll run out things to kvetch to you about if you don't counter her (even if you know she's wrong, just agree and continue what you're doing)
The passive-aggressive side of me has also dealt with the intrusive/judgmental questions by AGREEING with the asker. Tends to put them on the spot. I hope you try it sometime with this person...
It worked with my Mother in Law who thought I was being cruel to my cats since they were showcats. According to her, having them be indoor-only and not only giving them baths but using a blowdryer on them was cruel (Maine Coons have long hair and their coat is very important when showing...so my sheltie is like an honorary cat!). I agreed with her, went back to brushing my cat, and she had nothing to say.
It was glorious.
(And for the guy who told me to muzzle my dog, I did tell him that yeah, this GIANT dog can bite you, you better move away...it helped that several girls who wanted to take pictures of my Shiloh were also filming this man's date with death...)