Sometimes churches have Mommy & Me groups. I don't know if there are any churches near you that have one, but it might not hurt to call around.
There is a Moms Club in Hamilton. There might be kids of a similar age there, but there will also be kids of varying ages attending activities. But you and your child can go together to almost everything, except for Mom's Night Out.
If you go on Yahoo's website, you can probably find a playgroup in your area there. Look under Yahoo groups. If you don't find one, just start a Yahoo group of your own for moms looking for an infant/toddler playgroup in Hamilton.
Is there a YMCA or a YWCA close to you? They might have a group as well. I know there is a YWCA in Trenton, but that's probably 15-20 minutes from you.