Nothing will be open on Monday (besides the 'local' shops MummaB mentioned). Rockingham is a good 45 mins from the CBD and Mandurah is even further and I doubt either will be open on Monday. Your best bet is to shop on Saturday.
The CBD and Freo are the only areas open on Sunday and trading hours are from noon - 5pm. I live in Freo and there isn't really much in the way of baby shops except for Myer and Target. The city is about the same.
If you want a good shopping centre, I'd suggest Karrinyup (has DJ's, Myer and Big W), Innaloo (Target & KMart) or Garden City (DJ's, Myer and KMart). Karrinyup and Innaloo are north of the CBD (about 15 mins drive) and quite close to each other. Garden City is south, about 15-20 mins from the CBD. Public transport is not the best option so I'd suggest a taxi if you don't have a car.
The proper baby shops are scattered all over the place. Osborne Park (very close to Innaloo) has a couple and so does Myaree/Booragoon which is close to Garden City. They're generally situated with furniture shops, Bunnings, etc.
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