Hey,
Hope your new lil friend is doing ok.
It's good that you've got a heat mat, although make sure that it has enough space to move away from the heat if it starts to get abit too warm.
Also it does need to have more water than just a dropper, give it fresh water in a shallow dish. Please make sure that the duckling doesn't get too wet - as it could develop a chill and die (ducklings are not waterproof until a couple of weeks old).
I feed any ducklings that come my way on chickcrumb - it's basically crumbs that you can either mix with water or feed it dry. I tend to feed it with water to ducklings, as not only does it make it easier for them to swallow if their throats are abit dry, ducks are aquatic birds and would feed from or near water naturally.
If it's a Mallard, it should start getting it's feathers through at about 4 weeks old.
Mel X