DS did three years did at our local primary before moving to prep school. We didn't have the option of moving sooner as the pre-prep was full, but I was perfectly happy for him to spend the early years at primary. TBH I have no idea how much time they spent hearing him read, but I listened to him read every day so I didn't see that as a problem.
He is bright (his Year 2 teacher told me he was one of, if not the, brightest children in the class). Perhaps as a result of this we had a few problems with him causing some disruption in class - there were 28 of them and 20 of them were boys!
Since moving, however, he has really flourished. The school is excellent and produces fantastic results, even though it is not academically selective. One of the main benefits is not just the advantages of smaller class sizes but all the other activities they can do - choirs, orchestras, drama, archery, climbing, sports. They have fantastic grounds to play in, and no nonsense about banning conkers etc. His previous primary school had a lovely climbing frame built by one of the dads, but the children were never allowed to play on it in case they hurt themselves!
As others have mentioned not all schools are better just because they are private. We have two in our nearest town, and I wouldn't touch the other one with a bargepole. A good way to judge is to meet the children in the top two years and judge the school by the 'product'. The 6th formers at DSs school are very impressive. They are not at all arrogant and stuck-up. They are polite and self-assured.
I think you will find a lot of other children will start at year 3 (in DSs case over half his year started at that time). I don't think she will be at any disadvantage by doing her three years at a state school, and she will have a shorter journey in when she is still little. She will soon catch up when she moves.
DSs school is a 20 minute drive, but we have a school run with some other parents who live nearby. Some parents drive 50 mins to get there, so I consider myself lucky!
DSs school day finishes at 5pm. Lessons until 3 then tea then sport. He used to go on Saturday until 4pm too, although the school is changing this from September. When he started I found that he was actually less tired and grumpy than when he was coming home at 3.30. Also the terms are much shorter.
You will find it impossible to keep up with old school friends outside the school holidays. DS was sad to leave his old friends when he changed, but he was so excited about the new school it was not really a problem.
If you are happy with her primary school then I would leave her be, but if not then move her.
Hope this (incredibly long!) rambling helps .