As a native speaker I have never used that sentence.
This will be my motto for life. "My duck is having a rest." - Duolingo 2016
So if you visit another country (or currently live outside of Israel) and someone asks you to speak Hebrew, you have a new go-to sentence. Or you could try to start your own slang. How's your duck today? ;)
Well, if a gorilla can have a pet cat, why can't an owl have a pet duck?
Jokes aside, but what is wrong (grammatically) with "my duck has a rest" ?