We have a child in our neighborhood who is diabetic, and we have a number of parents concerned about sugar and fat overall. We don't give candy - we give toys and games, and they are so popular! Spider rings, slap bracelets, pencils and erasers, plastic airplane things, finger puppets (all Halloween-themed) -- all kinds of things from the party store. I had kids coming from across the street on 3 separate occasions AFTER Halloween last year, wondering if I had any leftovers! And I do - so I gave out a couple, and the rest I packed away, so this year I don't have to buy much at all.
You might see if your neighbors can have some things like that to give out to her - or even sneak them a few things ahead of time to hand out when she comes (tell them what her costume will be and make sure they recognize whatever adult or older kid who's accompanying her). They shouldn't make a big deal of it ("Oh, you're the little girl who can't have any candy" would NOT be a cool thing to say!) They can just put her treats/toys in her bag, and then she'll be thrilled with what she opens up at home. You could also give some sugar free candy to them to give to her?
Remember there's also gluten in some candy bars, so you're going to have to study up on the labels anyway.
We also used to give away a lot of candy - our neighbors pooled their excess and one of us either took it to the food pantry (not ideal - those families need real food) or to a dentist who liked getting all that candy out of the hands of kids and who made arrangements to send it to soldiers in Afghanistan and other deployments. We figured the servicemen and women deserved the treats and also knew how to brush their teeth! It was a great way to get the candy out of the house and really benefit someone else.
I also work with a lot of people (many in NH like you) who have dealt with Lyme in other ways and have not had to give up everything. You even say the doctor said it "might" help her recover faster, so it sounds like some guesswork going on. There are other ways to strengthen her immune system in a less punitive way.
Of course, you're assuming that we will actually HAVE trick or treating this year even with a storm coming! Last year, ours was postponed 5 days due to the snowstorm and power outages. Let's hope that doesn't happen!