Depends. If you're looking for a quick answer though, for me no it's not worth trading in your kit lens for a prime. Get a prime to complement the kitty, UNLESS you NEVER want to shoot anything else but portraits of your baby, EVER.
Otherwise, it's better to keep the kitty for everything else you need to shoot.
In regards to lens choice though, the Sigma 1.4/30 is a great prime, though for baby pics I'd argue that the SEL35 is just as good (and often cheaper especially if you can find one used).
Why specifically is a tad longer to explain. Read below:
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One one hand, the 30mm is a great lens overall, albeit a tad huge for my liking (and my bag capacity lol). Also it's "faster" (f/1.4) which means that it's capable of helping you take pics with faster shutter speeds (which freezes action better, considering kids often don't sit still) at lower ISO.
On the other hand, you don't get OSS (which the "slower", cheaper and smaller SEL35 does have), which helps stabilise vibration coming from your own shaky hands. That said, a faster shutter (thanks to that f/1.4) does help take care of hand-shake too everything else considered... at least under most circumstances.
However, being able to shoot at f1.4 isn't a silver bullet that solves all your issues. The DOF (the area that is in focus, aka "sharp"), can be razor thin at that aperture and it might not be optimal for you... and you might be forced to shoot at a higher f number anyway (to widen your DOF) - negating the advantage you get with an f1.4 in the first place... while NOT getting the hand-shake stabilisation you get with the SEL35 (which works at all apertures).
Also, while f1.4 helps freeze kids running around, babies don't really move all that much to begin with, in which case having OSS to stabilise your hands (again, at any aperture) might prove to be the better option in the end.
Heck, even if you get the SEL35 first, you should be able to save up enough to upgrade to the Sigma anyway once your baby IS big enough to run around lol.
However all this is just my non-expert opinion on the matter. YMMV really (as always), and others might have their own say so it's entirely up to you to decide.
Interesting point of view. Yes the OSS really puts the SEL35 ahead of the Sigma, especially if I wanna take videos of my baby. Thanks!