No you don't need to take it and recheck it in. 
Only if you are continuing on a low cost flight, you would need to collect your bag, check out, got the checkin desk of the low cost carrier and check in again. It is not advisable to take this route, because if you have a delay on your incoming flight, because of which you miss your connection, you would need to buy a new ticket. Since you are continuing to Stuttgart on klm, I expect that you will be flying on one ticket. You will see that on checkin jakarta the labels will already have Stutgard on them printed.

It might be beneficial to know your [EU rights][1]


  [1]: http://europa.eu/youreurope/citizens/travel/passenger-rights/air/