I would do the pre-k cause that doesn't mean she needs to start K next year. It's an option, but not a requirement, right? Or even if she does their K next year, you can always put her in public K the next year if you feel it's too rigid, too much work, or whatever. Yes, she'll be advanced if you do that, but being a different school I'm sure she'd be fine with the chance to just socialize with the other kids and make new friends.
FWIW, my daughter is in a Montessori school and she's now 5.5yo. She'll be the oldest kid in her class this year and she's probably a little advanced for someone going into K (which is essentially the grade she's in, though called 3rd year primary in Montessori) in that she can read, write in cursive, do basic addition, knows a ton of geography (like the countries in Africa based on their location on the map, continents, etc.), but I wouldn't say she's any sort of genius and she's definitely not bored in her classroom.
There is, however, a 4.5yo whose mother says she is bored and she wants her to be in the "K" program (so 3rd year primary like my daughter), but she has a January birthday so they won't take her in September. The difference is just half day vs. full day, where the full day kids do more advanced work in the afternoon with individual lessons. Anyway, her mom complained to the teacher and school that she wanted her to get more advanced work and the teacher said she really feels the child should just work on being 4yo and socializing and playing with the other kids. She can already read, write (at least in print, not sure on cursive), and I think do some basic math. The mom is afraid she'll become even more bored and then become a problem kid, but the teacher doesn't think that will happen and is really more focused on socializing at this point.