It IS redundant to define the kind of clothing in this particular sentence. You only need to write "I went to the mall to buy clothing for my baby" and the meaning is clear. Alternatively you could have "...buy baby clothes".
In the UK, clothing stores have departments: menswear, womenswear, children’s wear, ladieswear, kidswear. There’s also children’s clothing, ladies' clothing. Note that in all of these, the person part is plural. It is wear (or clothing) for all children (or men, women, babies). There is an exception to this in "baby": for some reason baby clothes and baby wear are acceptable, and I’ve never seen a babieswear department. Wiktionary.com gives it as a rare synonym. The only reason I can give for this is the verbal sound: men, women, children all end in "n", and the "s" follows naturally. It’s slightly less natural after "baby". Alternatively, it’s because of the accepted use of "baby" as an attributive noun An adjective or a noun?