Funny story - both my kids read early, but particularly kid #2. Yes, we had a hard time finding age-appropriate reading materials for her; be prepared for that.
Fast forward to third grade - she was eons ahead of the spelling lists her classmates were using, so her teacher encouraged her to use a dictionary to come up with a list of ten words she could study for that week, then the teacher would review it, and OK it. I volunteered in my kids' classrooms through fifth grade. I showed up one day to have #2's teacher pull me aside and tell me she had to have a 'talk' with her. Evidently, daughter was looking for the hardest words she could find in the dictionary, and came across a term that she didn't realize was a medical term. When her teacher saw it on the list, she asked her husband what it was because he was in medical school. Ends up it was the scientific term for some STD! Of course, #2 had no idea what an STD was, so the teacher had to navigate that conversation very carefully and explain to her she wasn't in trouble, but she couldn't use that word in her spelling list.
As far as skipping grades, although my oldest did not skip a grade, she did start K early, after two years of preschool (during which time she was learning to read). Cut-off in our state was 12 days before her birthday (every state is different in this regard) and in many other states, would be starting K based on her birthday. Anyway, her preschool teachers started encouraging us to see what our district required to bypass the cut-off date. We found out it would require a test and interview. She passed both with flying colors, so the district recommended she start early, although it was ultimately our choice. We talked with the principal of the school she'd be attending, and were encouraged. So we went with it. Yea, there were a few challenges socially, but she actually found her group of peers with kids who were within a month or two of her birthdate (and although she didn't share any classes with them because she was mostly in Honors and AP classes, she did share extracurriculars and electives with them), but had made the cut-off. She ended up graduating #10 in a class of 600+, so I think she managed OK.
Both of my kids had some amazing teachers; through 8th grade (high school starts in 9th), our school district had a program for academically gifted kids. This is where they really shone.
I remember when #1 was born, and the pediatrician visited us in the hospital. He told us, "Read as often and as much as you can to your kids, starting now." And we did. I'd like to think that had a part in their early reading. It was one of the first pieces of advice I gave #1 when our first grandson was born last summer. That... and singing to them.