Would it be safe?

I have a two year old toddler who is driving me crazy, I mean writing on walls, saying no and being disrespectful. I am assuming it is because he has no other kids to be interactive with. I try to be interactive with my toddler but between breastfeeding, chores, exhaustion...etc I just want to sleep when baby sleep. I have a neighborhood park three blocks from my house I use to take my toddler to before I became pregnant.

Would it be safe to take my month old baby to the park? I figure my two year old will be happy to go outside and get some air without being confined in the house all the time. I am asking because baby did not get his shots yet and I don't want him to get sick or anything.