What is an appropriate age to let a child play outside alone?

My daughter is a little over 3½ (will be 4 in October) and wants to be outside a lot to play on her swingset, run around with the dog, look for bugs, etc. I just can’t stay outside all day.

We have a relatively small backyard, so I am able to hear her if I leave the door open with the screen door closed. There are trees surrounding three sides of our yard and the other side ends before the side of the house, meaning no one can see her other than our 86 y/o next door neighbor who is a very sweet lady.

She is a smart girl who can take care of herself pretty well. She found herself breakfast and entertained herself this morning while I was in bed with a migraine. She knows to scream her head off if anyone she doesn’t know tries to talk to her when her daddy or I are not around.

Do you think it is too soon, or is she ready?