Found it! My son is very boysey but has no objection to girl protaganists. I even read him an abridged version of Heidi. I might even try him with my huge collection of Noel Streatfield or The Little Princess.
Chapter 1 starts on page 7. There's a picture of her house in the country and her (in Victorian clothing) going into the room with the telescope.
I like the opening sentence
"Rebecca lived in a big house in the country. At least it seemed like a big house to her, but then she was quite small."
Its the 11th day of the school holidays and she is bored, and annoying her mother with moping around the house. Her mother tells her to play in her room.
She goes upstrairs and tries walking with her eyes closed on the landing and crashes into a vase. It breaks and water is everywhere. Shes says it's not fair and she will get blamed for that.
(I always worry that reading books I loved as a child or teenager will ruin them for me as I will start siding with the parents. Am sure if I re-read Catcher in the Rye I will just get irritated with Holden not identify with him).
She closes her eyes again and ends up outside her father's study. She knocks, no answer so goes in. He has a brand new astral telescope which she has been forbidden to touch.
She's does touch it and sees one star outside the window. She bets the people on that star aren't bored and are having exciting adventures. She wonders if she will be able to see them through the telescope. So she looks. She wishes she could go there for a visit.
She then has a feeling that someone is looking at her from the other end of the telescope in the star. She would then appear to be very tiny.
Then its page 9 which you perhaps have? She starts to feel smaller, the star becomes larger and brighter. She reaches out to touch it, then she has a whirling feeling and a buzzing in her ears.
Then its all over and she opens her eyes and she in a place she has never seen before.