Painting Plastic

There is a spray paint made specifically for plastic by Krylon called Fusion that works fantastically.

There are fabric paints, that will give texture to a surface.
Its the kind that is from a squeeze bottle.
You need to use the search words "dimensional fabric paint."
These are great for adding details and "drawings" on things, and gives a "puffy" type texture to the surface. And the squeeze bottle has a fine tip and is easy to use and "draw" with it.
I have used this for various art projects with different mediums.
It does not have to be used, only for fabric.
It will adhere to plastic.
I have done it and with my various art projects.
But, it is not for "painting" an overall, background.
But for details and giving texture to the piece.
These fabric paints are non-toxic.

OR, use Sharpie permanent markers.
OR, use, glitter glue.
Any of these can be used to decorate even plastic surfaces. And it adheres to the surface.
You do not only have to use traditional paint.

OR you could try "glass paint pens."
Or "Sharpie Paint Pens."

Again, you do not only have to use, "paint."
There are many mediums to do what you want.

And, last but not least: you can also use fingernail polish, to decorate surfaces like plastic.
And use a fine or narrow paint brush, to do so.

Those are the ones for really little kids, right? Anything you add will probably get picked at and chewed on, so make sue it's non- toxic. Those things are about at my limit of visual and audio stimulation, so why you'd want more of that is beyond me, but hey that's me not you. Good luck.

There are several spray paints such as Krylon with a formula for plastic. You can also use the new duct tapes with funky colors and patterns. To be honest, if your daughter mouths things (and mine did at that age), I would not paint it.