My baby is sound asleep for hours and I'm worried if he/she is breathing.
「熟睡する」「ぐっすり眠る」は以下のようにも表現ができます。
sleep well
sleep like a log
sleep deeply/soundly
sleep like a baby
My baby slept well last night so I didn't have to wake up every two hours.
(昨夜は赤ちゃんがよく寝てくれたので2時間おきに起きなくて済んだ)
My brother is sleeping like a baby.
(弟がぐっすり寝ている)