"Baby, fall asleep already!"
Translation:Bebo, ekdormu jam!
I think the construction is simply wrong in Esperanto. "Jam" says something already happened. "Ekdormu" in this sentence is talking about something that might happen in the near future. Combining them is not an elegant use of the Esperanto language. I understand that it might be convenient for the English speaking Esperantists, but it is wrong to copy these strange sentence constructions to Esperanto.
It's quite typical of US English, but sounds strange to British speakers. As far as the course is concerned, it should certainly be an acceptable answer, but the intended meaning may not even be clear to a British learner. I'd say your suggestion "Hurry up and fall asleep!" is better; you should definitely suggest it.
In fact, even the Esperanto sounds odd to me. I'm just canvassing for expert opinions now... https://www.facebook.com/groups/duolingo.esperanto.learners/permalink/477487179079971/
Usually by swearing. "Baby, for goodness sake go to sleep" or some ruder version of that: https://en.m.wikipedia.org/wiki/Go_the_Fuck_to_Sleep
Everybody here is discussing how odd the sentence sounds from esperanto to english but seem to be forgetting that esperanto is model as a romance language, with very few Germanic words. As such let's all remember that in Italian, Spanish,Portuguese, French an Catalan the "ekdormu jam" would be a very natural way of speaking.