I grew up in an area where every other house had dozens of guns. Surprisingly, we didn't have a school shooting every day. In fact, we had none. I'm not using anecdotal data to support any argument, but if it were indeed the case that more guns = more baby and child killings, then I wouldn't be here to write this comment.
My main concern here is the erosion of natural rights based on the premise that it is "for the children", which is a trope. It's been used for all manners of privacy violations, from indefinite detentions, proposals to ban encryption, PRISM, etc.
If you genuinely care and have an open mind, you'll see it's extremely dubious as to whether enforcing more restrictions would have any effect, barring throwing the Constitution in the trash and seizing everything. Conversely, we can think of the children and ban cars so they stop dying in car accidents, because no more car accidents will happen.
I'm okay with incremental positive change, but they have to be data-driven and made respecting the Constitution. The US got this far due to its framework, its shared values on freedom and liberty, and lack of an oppressive, overreaching government. It derives its success from the freedom of its citizens to chart the course of their life, not from the nanny state telling them what they can and can't smoke, shoot, eat, code, read, write, or drive.