Little children who are obsessed with school may be expressing a real and abiding desire to go to school, and this may indicate that home education would be a selfish choice for their parents to make.
But I wouldn't bet on it. Kids fantasise about living different lives for all sorts of reasons. That doesn't mean they grasp the reality or that it is what they actually want to do.
When I was three, I wanted more than anything to be a Sioux brave. Was that a pretty clear sign that bringing me up as a little girl in 20th century style would be more about my mother meeting her own needs than mine?
When my daughter was four, she wanted to be a baby.
When my friend's daughter was five, she wanted to be a dog.
When my daughter's friend was six, she wanted to be a mistreated Victorian orphan. Her mother unaccountably declined to feed her stale bread and watery gruel, dress her in dirty rags when she went out, allow her to sell matches on the street corner, or speak cruelly to her in public.
Now, to my mind the only difference between these fantasies and your dd's school fantasies is that school is the norm. For that reason, you will get accused by some people of selfishness if you don't let your daughter try school. That doesn't make school a place she necessarily needs or wants to go.
I wouldn't have prevented my older daughter from trying school at four if she had really wanted to go, but I did make a point of taking her to home ed activities so she could see a positive alternative to school. Fortunately the school interest ran its course when something more appealing came along.