I think that your duckling is probably depressed because it is on its own. I have had the same experience last year with a rescued muscovy who became very sad and lay down and stopped eating at about a week old
I advise you to get yours out of the brooder now and hold it close it you, dipping your little finger in water and then in the duck crumbles and offering the little finger to the duckling, encouraging it to eat. Then hold its bill into a cup of water so that it takes a little water.
I held and hand fed mine, Daffy, and then had him on my table in front of me while I was working on my computer for nearly 4 weeks. Once he was being held and given lots of attention, he quickly perked up. I gave him a mirror which caught his attention but within 4 hours he worked out that wasn't a real duckling. But he could see me sitting behind him and he used the mirror to be sure I was there.
I used textured shelf lining paper over newspaper on the tabletop, so that he didn't slip when walking, and mopped up poop straight away with a tissue. I used various little toys such as colored plastic bottle tops, an orange pingpong ball, and later parrot toys. The toys were mainly dropped onto the floor for me to pick up!
Daffy thrived once he got the close attention and handling he needed. When he had to go into his brooder, I put the brooder on a chair next to me so that he could look up and see me. He was very closely bonded with me [not imprinted] and when he was big enough to let out on the floor, followed me around. He swam daily in a washing up bowl [but didn't like it, only enjoying the drying in a towel afterwards]
I tried to find him muscovy duckling friends but the only ones of his age I found would have involved a 4 hour drive to get them and a 4 hours drive home. I was not doing that with a sick duckling in a box on the front passenger seat. When he was 5-6 weeks old, I found that my local wildlife rehabber had ducklings including other muscovies and a pekin with a deformed beak from a raccoon attack. I took in another muscovy drake and the pekin, and this year I rehomed a second pekin drake.
The photos show Daffy when he was first found --the day before I took him, then when he became depressed and laydown in the corner of the brooder and didn't eat or drink; Daffy with the mirror and playing on my table in front of my laptop; bathing, snuggling up to me on my shoulder where he spent a lot of time sleeping and nibbling my ear; in his brooder on the seat next to me where he could look up and see me; and as he is now: big lump of soft muscovy!!
Please handle and hand feed your duck now and get back to us with updates.
