Yes, it seems like it. You probably don't need a new set, just reuse the old one.

They are very durable and easy to clean. I even like the way they look specially on the old style steel bicycles. It also fits better in the small hand.

That's a nice looking bike and if you take a good care of it, it'll last a long, long time. If you are thinking of replacing the brake calipers, make sure that the new ones are double pivot. Single and double pivot are very similar in the appearance but the stopping power makes a big difference.