Ma perchè non traducete letteralmente e non la piantate di fare la gara a trovare risposte alternative come fosse lo scopo di questo programma?!
Andrò a dormire è più corretta, uno può andare a letto anche senza addormentarsi
In English, "go to sleep" can either mean "go to bed and lay down ready to sleep" or "fall asleep" - I went for the second interpretation and translated it as "Dormirò" which was marked wrong. Anyone else think this should be an accepted option? :)
For me "I will sleep now" is not a natural sentence.
For your first option I'd say "I'm going to go to bed now". And for the second "I'm going to go to sleep now". (going to for intention in the future)
It seems Italiam only uses "andare a" in a limited way in this sense, so yes, I think your suggestion should be accepted.