You are right to be concerned. Lead contamination is a widespread issue, which most people don't even know about. Our house was built in the early 1900s, too, so when we moved in, I had the soil from several areas in the yard tested. The results were chilling. There were high levels of lead everywhere, but the worst areas - closest to the house - were so bad that we jokingly started calling them "the EPA areas", because the advice listed under their ranking was "contact the EPA immediately"..... We had several tractor trailers full of clean soil delivered and laid on top of the entire yard, covering it by about half a foot. It was a massive operation, but that was the only way we'd feel comfortable raising children in that yard, not just animals. We now have a strict rule of no digging in the yard (except when we plant trees, carefully, but absolutely no digging by the kids). We don't have a dog yet, but when we get one eventually, we'll need to do some serious "no digging" training. Our chickens don't dig deep enough to reach the original soil of their run, and they don't leave the run, so they've been healthy so far. Periodically when I have a sick chicken that merits a blood test at the vet's, I've had them check for lead, and the results have been normal, so that puts my mind at ease that our efforts (and expenses) have helped.
Our neighbors across the street were planning on having kids around the same time as us, so we told them about the lead and advised them to have their yard tested, too. And sure enough, they had dangerously high levels of lead in the soil as well. So they did the same thing and brought in clean soil to cover the yard with. Our yards aren't all that big, so it wasn't an impossible task. People on more land will find it more expensive, but also the areas with more land (out in the country) aren't as polluted as small yards on the outskirts of big cities like ours.