cecilau,
Going to Taiwan with BB is not hard if you go to Taipei only.
I went with my BB twice there. The 1st time my girl is 3 months old. The 2nd time, my boy was 7 months old and my girl was 2.
However, remember to bring carrier or BB car (if not heavy) with you. Especailly good in airport and shopping mall. Also, bring medicine especially for fever and some toys.
Tell the airline in advance taht you go with BB and order BB food for your BB. THey will have better arrangement for you. Remember call in advance and reconfirm when you check-in.