When I transport rescued wild ducks, I used small pet [cat or dog] carriers. They are small enough to stop a frightened wild duck from fighting its container. THey are only moved locally -- short journeys in such a small contained.
When my son and I transport our duck(ling)s we use a deep plastic tub like the gray one in your photos. Little ones just sit in the bottom. Four of our adult ducks now like to stand up in the tub [it will only take 2 of them at a time] placed on the front passenger seat strapped there by the seatbelt, to see where they are going! But the three adult ducks that are not used to traveling, when they have had to be moved, have gone in the deep tub in the back of my van with a sheet over them so that they are not frightened by the changes outside the window.
From what I can see of your gray tub, it would be big enough for 3 but not all 4 ducklings. If you do not have a second plastic tub, you might get a big cardboard box and put two in the gray tub and two in the carboard box.