Leaded solder is banned in Europe, California, and various other places, but that's for environmental reasons not direct health problems.
The solder on modern pins, and most solder you find at the store should already be lead-free.
Even if you're using the old stuff, I wouldn't worry about breathing it. It's not going to go airborne. Keep it out of your mouth, wash your hands, and you'll be fine.
...But I *REALLY* don't recommend using old-fashioned leaded solder in a house with little kids. Here's why : You're going to screw up. You're going to trim a wire and lose it. Bits of solder will wind up on the floor or under the couch. If your kids are still in the put-everything-in-their-mouth stage, this is bad. Like leaving some lead paint flakes laying around.
Get a spool of the lead-free stuff, and a soldering iron hot enough to melt it properly.