I know that ~もくそも(ない) is is an expression that can mean: not at all; not even a little
However I'm still confused at what もクソも in 何かもクソも寝るだけだよ means.!
This ~もクソも(ない) is a dirty version of ~も何も(ない) described here and here. In slangy speech, 何 in ~も何も can be replaced by クソ, ヘチマ, へったくれ, etc., which are basically metaphors for crappy/meaningless things (see this discussion in Japanese). In this context, he is saying asking "何(か)" to him is meaningless.
何してるの?
What are you doing?何かもクソも、寝るだけだよ。
= 何かもクソもないよ、寝るだけだよ。
= 何かも何も(ないよ)、寝るだけだよ。
Why d'you ask? I'm just about to go to bed.