What is your plan for the air conditioner unit? That plugin and controls just at here eye level is a huge red flag for me safety wise. What is the unit made out of? The doors do not look like wood? What are the gray stripes? Painting it in fun colors might be nice.

I wouldn't paint it, but you could change the handles to ones that pull in the colours from her comforter, etc. There are fun, removable wall decals available that would add interest to the doors of the unit. Check them out online -- there's lots of them.

The storage will be great! Lucky little girl !

I'd remove the strip of metal at the handle level. I like the idea of using colorful handles, rather than painting the storage.

Can the gray parts be painted?

We may just pull the doors off and keep the shelving, as the unit’s in generally good shape, but the doors just look worn.

I think that's a great idea.

You can also line the back of the unit with paper or fabric. If you cover cardboard cut to fit first, it can be removable or changeable as she gets older. If you Google it, you get a bajillion DIY links to blogs.

Pulling the doors off would definitely work. The storage is good, I wouldn't consider painting it since wood/laminate doesn't work well with paint.I also agree with changing the A/C unit and go for the ductless.