。
She has her hands full with the baby.
Literal
She [topic-は] baby [with-で] hands-full is.
手いっぱい (ていっぱい) means 'hands full' or 'at full capacity' — literally 'one's hands are full.' It describes being so overwhelmed with something that there's no room for anything else. The で marks the baby as the cause of being overwhelmed. This mirrors the English idiom 'hands full' remarkably closely.