"Back in the old days" kindergarten was to learn socialization, numbers, colors, practiced writing their letters and number recognition, practiced writing numbers. But they also went half day and had nap time, which have gone by the wayside as well. Things have changed, and we can't go by what we did. Now preschool is where you learn all that, and kindergarten is learning to read and stuff like that. They expect your kid to be socialized, know how to play and handle simple situations with PEERS (not just adults) by the time they enter school.
You should be able to put your child in preschool starting when they're like 2 years old. Pre-K is when they are 4 or 5 (depending on birthday and when they're starting kindergarten). There should be lots of places you could go for preschool (the YMCA, the Goddard schools, any private place like Primrose Academies or something like that). Check at your local daycares, and I'm sure they have preschool (it's basically just daycare for little kids, but they play and learn how to play nicely, handle little relationships with kids that are not necessarily the same as them, how to share, etc and they should be learning like one letter and color a week, counting, stuff like that. At age 4, my son goes to a daycare 3 days a week and they discuss weather, where clouds come from, how to make rainbows, colors, they have all learned how to write their own names, recognize their names on things, trace a letter a few times and then practice writing it (one letter a week) with show and tell with something of that letter every Friday. Simple stuff, but he's actually picking up on some good things. Next year instead of kindergarten (because of his birthday, in October), he'll go to pre-K. I was tempted to put him in a private school for pre-K to make sure he's academically ready for "real" kindergarten year after next, but I've since changed my mind. I think it'd be better to save the money (3 times the cost of where he's currently at) and put him in private school LATER (like 3rd grade or so). But that's a choice you make based on your own child.
What I'd suggest is to get info on the school standards in your state to know what is expected and start working on it with her. Most of the education should come from home no matter what their age, in my opinion. I got our state standards for kindergarten (but he will be past that by the time he finally gets there)---stuff like sequencing and recognizing patterns is something we haven't tried yet though---then I just made a list of the classes I remember and what I think is important: Bible, math, science, reading/writing/spelling, history, geography, foreign language, physical ed/health, art/music, social studies, character development, volunteerism, all of it. I try to incorporate little fun things throughout the day that will touch on all of this. Cross learning is great and should be used much, much more in "real" schools too. We can have a lot of fun reading a story, playing/pretending with that theme, breaking out a map and learning about where the story is set and some history or what the people do there, etc. I'll get off that soapbox though....that could last forever! But yeah, preschools are everywhere (daycares or a private academy)....pre-k is your choice, whether she stays where she's at or goes to a more "exclusive" place, or is eligible for a school-based pre-k (some schools have that, but most often for lower income or children that are a little behind, unless the state funds the school district well). But you can get the state school standards online and make sure your child has those bases covered whether you put her in preschool or not. I chose to do so because it's good for him to play with friends that are peers, not just adults, and also it gives me time during those hours to play with my younger son and let him have that time to feel like he has all the attention, as my older son had at that age.