If we live in an older home, should I be concerned about my baby getting lead poisoning?

Yes. All infants should be checked for lead at ~1 and 2 yrs of age. In older homes, be careful about peeling paint, a common source of lead poisoning.
Be mildly concerned. Lead is a naturally occurring element, and was used in homes for generations before the most recent 30 years. So, children growing up in older homes will likely have more lead exposure than kids living in new homes will have. A blood lead test is routinely done at age 1 year and 5 years, in communities with elevated lead exposures. Avoid raising a baby in a home during dusty remodeling work.
Yes. Despite the fact that lead-based paint has been banned in the US since 1977 (and in Europe since 1900!), it's still a huge environmental health concern for small kids. Small kids live close to the ground and explore the world with their mouths. An older house represents a risk. Your medical provider will likely check a lead level at 9 - 12 months of age.
Keep it in mind. And make sure your dr knows the age of your home. Children routinely get tested for lead at 12mo and 5yrs, but if your child exhibits symptoms your dr may test earlier. Babies may eat old paint chips containing lead and this can build up in their bloodstream over time causing neurological problems. You can test your walls for lead exposure in the paint.