"Il n'est pas à la hauteur de ce travail."
I think "ce travail" is part of the idiom, therefore "he is not up to the task" is all you should say.
I think the French idiom is just "(être) à la hauteur", which means ≈ being able to do something (this is what my dictionary says too). Example: Il est à la hauteur de la difficulté.
But in English there is an idiom "up to the job" which also means being capable of something, and this creates confusion. English example: Barcelona weren't up to the job against Bayern (this is about football).
Maybe an idiom in French, but it's just strange in English (it's not an English idiom). In fact, in English, that says something very different. It implies the person is asleep.
The other suggested English solutions are more accurate.
If they had "not up TO do that job" I would agree he wasn't out of bed yet. Otherwise I think the solution offered is fine. But I think mine and others were correct as well.
You're correct in the main example, I was referring to the one posted above by petitlapin, which fits what you quote.
He is not up to the task of doing this job. It does have an awkward English translation.