I tried my best to design your daughters bedroom according to your instructions and desires, and I hope I managed to do so.
First of all, since Giulia is right-handed, the desk has to stay on the same place, so that the light from the window comes to her left side. I proposed a different position for a more subtle bed. I think that the room will have more free space this way , which makes it a lot more functional. You should just move the air conditioning unit to the other side of the same wall, so it doesn't blow into her, when she lies on the bed or sits by the desk.
Since you sad that your daughter likes to study, I equipped the room with bookshelves, 180cm long desk and hanged bookcases above the desk. Desk lamp and wall lamp on the bedside, make study areas appropriately lit.
Proposed custom designed built-in wardrobe is more functional then the one you have, with drawers on the bottom, spacious clothes space in the middle and a separate compartment on the top to store some things she doesn't frequently use. The only furniture piece besides the wardrobe, that is supposed to be partially custom made is the headboard unit. Detailed drawings for this pieces are attached.
I combined light wood and Lila color for the furniture, to give the room a bit of personality, since the walls are to remain white, as you suggested. The floor can be covered with a carpet, but it doesn't have to; It's your choice.
As for the armchair, I think it is not a good idea for a room like this. It would make it seem cluttered.
You do not have to use all the furniture pieces that I proposed if you do not like them for any reason. You can find alternatives, or order custom made pieces that mach the style and colors of the proposed, and create the same visual effect.