The first idea was to take of the steel rod and replace it with a longer threaded rod, drilled thru the sides and kept in place with 2 nuts on the outside. Yes, it would have made it very sturdy, but it would also change the looks.
The second option was to just fill make the hole bigger, fill it with a wooden plug and drill the same 13mm hole again at the same spot. The trouble however in the first place was probably the just 1 cm dept of the hole.
So I decided to go for the third option, putting to little external blocks on the inside of the stepladder's legs. To protect the wood I felt it would be a good option to put a few copper pieces of pipe inside the wood so the steel bar would pivot in those.
It turned out a good solution. The rod goes 2 cm deeper in to the holes on both sides which makes it a sturdy connection.
After a coat of paint this repair won't have changed much to the looks, and this little stepladder will be a safe device for many years to come, for instance to put the Christmas decorations up!