You asked about toys. There are several duckling life enrichment options, depending on size. you can make tunnels from empty cardboard boxes [eg cereal boxes, for them to run through. You can make steps for them to run up from flat disks of wood or tile. Make sure the steps are stable and don;t fall over. there are various brightly colour wooden toys with bells retailed for parrots that they can peck at. When I had a rescued duckling I was rehabbing and it didn't have ducky friends, I used parrot toys, a mirror and simple things like bright red plastic milk gallon tops. The duckling loved picking up the red milk tops and dropping them on the floor for me to pick up and give back. My duckling also liked rolling a pencil across my desk. When swimming in the bath, I have two plastic lattice balls with a bell inside each. Ducklings can peck at them and push them around. One of mine liked to trample them down into the water.
All these suggestions need space in your brooder. If there isn't space for them, then that is likely why your duckling might be bored!!!
I am going to have to what for my dad though. 
(I miss the tiny babies). and I'm still not sure on the breed. She has been panting a lot
(mouth open and rapidly breathing). They have
I do hear beating when I hold her to my ear (it is much louder than the other ducklings). There is no discharge from her nares or eyes, and her eyes don't look swollen. Her appetite is pretty good from my knowledge; her energy level is great (she with run around the brooder and go swimming when I take them outside every day). Here's a close up:
