It seems to me that it would be perfectly acceptable to also translate this as "I don't know what time it is," since "I do not have the time" isn't exactly in common usage to convey that meaning in English (at least in American English).
Literally, is this not "I don't have the hour"?
Up until now, on Duo, "I don't have the time" has been "Je n'ai pas le temps." Now, suddenly it's "Je n'ai pas l'heure."
Do they have the same meaning--or not?