I'm going to assume you're in Ontario (sorry if this is wrong). My first recommendation is to find out what your school board has in terms of gifted programs and what age they start. If you're open to changing school boards I'd also check out what they have for options (I'm in Ottawa so we have 4 school boards to compare). I'm not aware of any that start in JK or SK but there are a few boards that start in grade 1. You might want to check out the forum at
http://www.abcontario.ca/ which might have more info about your specific school board.
I have a gifted DS7 who is in grade 2 and a non-tested DD5 in SK. I spent a lot of time in both of their classes so I'm reasonably familiar with the Ontario Full Day Kindergarten program. The expectations are set across the province and in many cases are far exceeded. Most of the reading was done 1:1 with a parent volunteer out in the hall so it was very easy to differentiate and have kids reading at their level. DD had 29 kids in her class so her teacher and ECE generally had stations for most of the day and worked with small groups which again lends itself well to being able to differentiate. The new program is very play based and at first glance looks like a bunch of kids just playing but it was surprising just how much they did manage to learn. TBH the kindergarten program is easier to differentiate than grade 1 when they generally start doing more worksheets that are explained as a group and then done at their desk while the teacher walks around.
IMHO differentiation is HIGHLY teacher dependent. We've had some teachers that are fantastic and were able to keep all of the kids engaged. Others weren't and the class was wild. It also highly depends on the kid's personality. My DS is 2e and can be highly disruptive if he isn't kept appropriately busy. He is far more challenging in a class since he often refuses to do work that is "boring". DD on the other hand is much more of a people pleaser and loves the social part of school. Neither of them is learning much academically at the moment but we finally have DS not acting out and reasonably happy and DD is happy. They are both learning a lot of soft skills and for DS he's learning ways to cope and work around his LD which for now is what we're focusing on. We will likely have to change stuff in the future but for this year we're ok with that. We do a lot of learning after school.
My advice would be to go in with an open mind and see what they say. You might want to take some examples of her work/ability in case they haven't noticed and see what they can do for her. You might also want to inquire about testing. Our school won't test until grade 3 so we did it privately. Having concrete results went a long way with our DS's situation. We were no longer pushy parents that thought their kid was super smart. In his case the 2e hid a lot of his abilities in a school setting so they were a bit stunned by just how high his scores were. They still aren't able to fully meet his needs but at least they're trying and are working with us to try to improve things.