I was thinking that it is difficult to find a wide place in Jakarta (except Ragunan) that can help Katya releasing her energy. And few months ago my friend suggested me to go to PlayParq, an outdoor park that has some activities for children. They actually have two branches, one in bintaro and one in Kemang.
The tariff is not too expensive, about IDR 90,000 for the baby, and for their parents are about IDR 10,000 per person. I am sure that your child will really love to play there (at least the one in Kemang – I have never been to the one in Bintaro). They have outdoor and indoor activities, from building lego, swimming pool, flying fox, slides, and bunch of other activities.
Please note that the fountain area (as you can see in the picture) is a bit not safe in my opinion. Your kid can slip and hit the pillar. The others are safe, the floor are also have rubber layer to protect your child from falling.
Please note that they only open after 14.00 on Monday – but the tariff are cheaper, about IDR 60,000 if I am not mistaken.