basilisk4, I have a baby on the way (due late April) and so I have started worrying about some of the concerns you shared.
Of course, the first thing will be not to allow him access to any firearm, for the next few years. But I always worry about Murphy's Law, and how to layer defenses.
For that reason, I'm switching my primary carry from the 1911s and CZ75 variants I've normally preferred, to the HK P7 PSP.
Not that I have any intention of allowing a baby or toddler to gain access to my handgun, but just in case something should happen that would thwart my intentions (for instance, sustaining a head injury while carrying, when with the kid - as an extreme example) I think the squeeze-cocking grip will be both too large and too heavy for any small child to manipulate. The P7 can't be fired if the squeeze-cocker is not depressed.
That said, when my handguns are not on my person, they are in my gun safe, or in the console vault in my truck, and locked up.
Edit: For both basilisk4 and the OP, the other point is that if you can find a P7, you should be very comfortable with the safety of carrying it with a chambered round, but you should also like the trigger and the low bore axis.