I am here in Taipei until December studying Chinese at Shi-Da and I brought along my 2 year old.
I still haven't figured out the babysitting yet. I was lucky to rent quite a big apartment in Xindian, so there is also the possibility of letting someone stay here during our time in Taipei in change of 4 hours of babysitting from Mo. to Fri. (free afternoons, evenings and weekends, own bathroom etc. ). I would be quite happy about a personal recommendation since I don't really want to let anyone come live here with us and take care of my son! Maybe someone knows someone who knows someone who likes to be with children and needs a place to stay for almost no money!
Or maybe there is someone in a similar situation and we could get connected.
I will be happy to get replies..