Hi Nes,
I can't remember everything my kids were doing at 13 months but I can tell you that our first would sit for long periods of time listening to and looking at books. When he wasn't listening and looking, he was exploring. He ran early and had a natural stride. We often heard how active he was from other parents. It was embarrassing at times to have other parents compare their child to ours but I would point out that that was what he was interested in.
Our second was even more active, something we didn't think was possible, but instead of liking to listen and look at books, he only wanted to explore on his own. It was very frustrating for me because I had gotten used to his brother and couldn't figure the second one out. He spent a lot of time watching trucks, drains (water flow in general), and paying attention to garbage cans.
We would take the kids to the zoo a lot and the second would run to all the garbage / recycling cans, drains, and any other type of infrastructure while the first carried on about the animals. Both noticed small changes in their environments. We tried to take them on walks, visit museums, and talk about how things work. I've found that helping my kids develop their strengths and interests has been much easier than trying to force them to do things they don't want to do - they let us know when they are not interested and I have learned to step back and watch.
There are lots of great resources available on this site and it's also a great place to be able to talk with others without feeling like you're bragging.
Every child is unique and yours sounds wonderful. Hang in there, it's likely you are going to have a very active ride...
Added: Both our kids attended a full-day play-based Reggio Emilia program from about 3 months to kindergarten. They learned important social skills and had the opportunity to do amazing projects.
http://en.wikipedia.org/wiki/Reggio_Emilia_approach
