Yes, it should be wet but not soupy. You don't have to do it, but's easier for them to eat it that way. Just make enough that lasts them the day (or half day if you have time and will remember to make a new batch). They will fling a little bit but as long as you don't make it too soupy it shouldn't make too big a mess.
Why did he buy duckling starter for the quails? The quails need a gamebird starter (even higher protein).
If it makes you feel any better, I got ten Indian Runner ducklings last week. Three of them are now about 2/3 the size of the other seven, if even that. My previous batch of Muscovy ducklings, one was also a "runt" - somewhere between 1/2 to 2/3 size of the rest - but they are around 4 months now and everyone is fine. Sometimes there are just some that develop slower. Sometimes they catch up and sometimes they stay smaller. The most important thing is to watch for signs that they aren't feeling well and to ensure they aren't being bullied in any way.
Does she splash around and bathe normally when you give them a tub of water to play in?