Just check your abdominals have come together before you do any running. Do the stomach crunch thing (lie on your back, knees bent, feet close to your bum and roll your head and chest upwards in a curl - put your fingers around your belly button and check there isn't a gap between the rectus abdominus muscles). If there's no gap you're good to go, although build up slowly. IF there is a gap of two fingers or more then running may well 'fix' this separation, which can lead to back problems, abdominal weakness, etc.
I ran 12 weeks after my (grisly, complicated) caesarean and although I was desperate to get out there and get running again I'm glad I didn't push it and run any earlier as you really can wipe yourself out and, if your stomach muscles haven't come together, can make things worse. Before pregnancy I'd been super-fit and run for years and, although I planned to run through pregnancy, a difficult twin pregnancy put paid to that. The first run was really hard but I took it slowly and listened to my body. I made a pact with myself that if my stomach (or I) felt odd at any point I'd just stop and do a gentle walk and then build up that way. In the end, I was okay and it was only months of a killer stitch that I had to work through that really gave me any problems.
My tip is to build up slowly by factoring in some small walks and then building up the distance and speed over time. If you factor in pushing a buggy/pram you can really help to build up your base fitness/strength which will make running less of a body shock when you start. I also did some gentle pilates (not all the abdominal ones though as I was advised to avoid them until four or five months post birth) and they also helped.
Waffling response but what I'm trying to say is that on paper 13 weeks would be absolutely fine but just check your abdominals first. If they're okay and you're feeling well in yourself then I can see no problems. Running is an excellent way of getting fit and I felt pure JOY when I got my trainers back on (although the first run in nearly a year almost killed me!).
Good luck.
Kx