My daughter started kindergarten at 4. Luckily, she was able to enroll in summer school, for free, and she got to choose things she was interested in. She chose arts and crafts, drama class, science classes. Each year, they had a kind of "yard sale" at the school to raise money for supplies, etc.
I donated numerous things and I also bought numerous things. There was a lot of great stuff and all proceeds went to the summer programs.
I don't know if you have anything like that in your area, but it's worth checking into.
Like you, I didn't want my daughter in front of the TV all day. We went to thrift shops that had 25 cent Fridays. All clothing was 25 cents. We had amassed quite a collection of play dress up clothes, hats, beads. I altered a lot of dresses to fit her and she loved having a little neighbor girl come over and dress up. I would serve them herbal tea and cookies. They had so much fun.
I, personally, think that all children should take swim classes. I had a hot tub that was big and like a pool. My baby son who came along when my daughter was 10, was a natural in the water. He went on to win medals on a swim team. Swimming is so important for the safety issue.
I do think that some things are very beneficial, but I also don't think that every minute of every day needs to be so structured. Kids need time for non-structured creative play. Play cards with her. Old Maid, Go Fish, You can use a regular deck of cards to play "The Memory Game".
Give her a tape recorder and let her make up stories. Write them down and keep them in a book.
I did that with both of my children and they are so precious to me.
My kids are older now, but they get a total kick out of reading their stories.
Have her help you bake cookies.
Have her help you make homemade butter.
I also gave my children a love for books. We went to the library once a week and chose books. My daughter, when she was an only, loved Nate the Great books. We read every single one of them.
While you have an only child, you have to find ways for her to entertain herself. Puzzles, coloring books. Dress up.
Where we live, the weather isn't always very good, even in summer. We had to get creative and I had to teach my kids to entertain themselves.
I bought Play Huts. They are really great for imaginative play. You should google them. I bought mine off a home shopping channel and they are the best thing I ever bought. They fold up to nothing, they've lasted all these years. My grandson can play with them when he comes over.
Make forts. Have a picnic lunch in the living room.
There are lots of things you can do that are fun and basically free at home.
Best wishes.