I agree with what Dude says. I think you've got a lot of latitude too. There are many ways to cover English, math, science, history, etc. No one says math needs to go in the sequential order that the public school uses or even that you cannot accelerate if warranted. As an example, you could cover astronomy for science rather than the standard Earth Science.
I also would say you can take a deep breath and try to relax. Yes, it's prudent to keep a portfolio or some kind of log for learning, but it's unlikely anyone is going to come after you if you skip over grade 1 standards for grade 3 standards, for instance, or dare I say with attendance. It's not like public school kids get docked or compensated in hours for fire drills or pep rallies when they should be diagramming sentences in English.
I don't know about IL, but kindergarten is NOT federally mandated. It's my understanding that homeschooling does not 'officially' begin until compulsory schooling starts. This means you don't need to submit any paperwork until you're child is about to begin first grade. Of course, double check.
As with homeschooling, some parents feel more comfortable sticking to a structured regime that does not differ terribly from the public schools. Others veer off or do a combination of structure/unstructure. Some go completely unstructured and unschool. There's a wide range today; and some people go back and forth with what they do. You will find your way and what works best for you and your family. Try to find some homeschool/unschool groups in your area and pick their brains.
There are books, websites, etc. that may be useful so the process doesn't seem so daunting and intimidating. Joanne Calderwood's book, Self-Propelled Advantage, and Cafi Cohen's book, Homeschooling: The Teen Years (which is a bit dated now) may be helpful to see how other parents document, structure or unstructure learning, etc.
A 2e expert last June/Jul recommended that my ds7 2e/pg use a general curriculum series for this year. Next week, we're doing something different because he finished the series this year. Nevertheless, I used a combination of portfolio/summary to document ds7's accelerated school work. I'm sure it was overkill, but then I'm a newbie to it
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