I’ve never heard of birds “playing” but you could get some parrot toys from your local pet shop and put them in her cage.
Many more intelligent species of birds really do play.. parrots, crows, parakeets etc.. just the same as human kids and monkeys. Even my ducks have a crazy half hour diving under the water and wildly swimming about like a speed boat.. I am sure they are having fun then.
My parakeets love to play with all sorts of things... and will swarm over any new toy put in... At the moment they favourite game is to run about with a cat ball and chase each other about to see which one can thrown the ball in their bird bath!!
OP
I keep ringneck doves which are basically the same as the collared doves.
They don't really play with toys as such.
I found mine get a lot of fun and pleasure from the following things:
1. Bathing. They love to splash about in a shallow bowl of water.. and will often sit and soak in there to relax.
2. Sunbathing. They like to sit in the sun and spread their wings out and go to sleep. Make sure they have a shade area to go into when they want to cool down. You can put the cage outside in the sun with a shade over half of it, or they will sunbath in the sunlight through your window. You can also put the cage out in a light shower of rain.. the dove will have a shower.. and spread its wings out in the rain.
3. Flying laps around the room and full speed.
4. Pecking for seeds and grit sprinkled on the floor. Easier if floor is tiles or wood lol.
5. Nesting. Whey your bird get old enough it will love to collect feathers, twigs and stuff and make a nest. It will also like to coo and dance to you or a large mirror if its a male. If female it will like to brood eggs (replace the real eggs with some fake ones or small white marbles, balls or stones).
Thanks about it for their play time, apart from them just being with you, preening your hair and fingers... and they like to be tickled behind their neck.
If you want to make you cage better for your dove.. replace the perches with 2 natural perches from tree branches.. one thick and one thin... these are great for the birds feet and claws. Include a sand box with sand and bird grit in it for your dove to peck about in... they even dust bath sometimes.
Hang a bundle of fine twigs, feathers, grasses from the cage roof for it to peck at.
Feed your dove some millet spray and bunches of seeding wild grasses... the dove will get entertainment form pecking at these for food and the seeding grasses are really full of nutrients and protein. Collect the grass from an area free of chemicals!!!
Can't think of anything else!!! Enjoy you lovely dove.