Indoors, I have found that the Canon produces better, more accurate portrait shots than the NEX 5R, which tends to overcompensate/undercompensate for lighting, leaving you with indoor shots that seem unnatural without further processing. This is just my personal experience (I sold a T3i for a 5R). Also, with the Canon, use the 'Portrait' mode and its pretty much auto; takes spectacular baby photos every single time. Portrait mode shots with the NEX aren't as reliable. You also have more (and cheaper) options for mounting external flash with the Canon. You can get a decent TTL flash for $100. With the NEX, a flash upgrade gives you only one option, and that option is notorious for quitting on you within a few months. Lens options are much more varied with the Canon as well. I also find the Canon kit lens to be better quality than that of the NEX. You're also not going to get much more portability with the 18-55 on the NEX 5R, unless you use the 16mm or get the expensive 16-50mm (might as well get the NEX-6). The 16mm has no zoom, so you will need to do a lot more walking back and forth. Also, using the viewfinder will give you much more steady shots.
I find video autofocus much better on the NEX, and I find myself shooting so much more HD video now. When we ask people to take our pictures on vacation, they are much more comfortable with live-view than using the optical viewfinder, but live-view on the T4i is rather slow. If you are OK with losing zoom, the 16mm makes the NEX much more compact than the T4i, meaning you are also more likely to use it in more places (and be able to find room for it in your diaper bag). One more thing going for the NEX is dashing good looks - the T4i looks drab in comparison (though some would say more professional).
In conclusion, having had the NEX for a while now, I'm finding it to be somewhat of an odd choice. Neither is it compact enough to fit in your pocket, nor does it have the lens/accessory eco-system that leads you to consider upgrading from a compact to an interchangeable lens format.
If you are not looking into upgrading lenses down the line, I would seriously consider the RX100. It is immensely more pocket-able than the NEX, and has better optics than the kit NEX lens. The only thing it is probably not well-suited for is telephoto shots. If you are looking for a more expandable option, I would choose the T4i over the NEX.
Very good advice. While the NEX and M43 (micro 4/3rds) cameras look appealing due to their small size, as soon as you start putting lenses on them they aren't much easier to carry around than a small SLR. You typically give up having a real viewfinder, and you give up a LOT of selection regarding lenses. Any camera using a very large sensor and interchangeable lenses will need a relatively large lens (for zooms anyway) and a certain distance between the lens and sensor, making it bulky.
I agree, if you want something portable/pocketable, get the RX100. If you want to change lenses and think you'll invest in a system over time, get a DSLR. Eventually, it's likely you might end up with both!
For stunning portraits/baby pictures, get a lens with a nice wide aperture for the Canon if you can. For a beginner I'd suggest 50mm f/1.8. For about $120 you'll be able to take stunning portraits!