Wheather & Preparation - Trip To Taiwan in Dec 2014

Hello, my family include a 3 years old kid, will go to Taiwan in Dec 2014 (14/12/2014 to 20/12/2014). What is the weather at that time ? We afraid that our kid cannot stand for the weather as I heard that there is no center hitter provided in indoor ? Please advise :
1) What we should pack ?
2) Which part of Taiwan that is not that cold ? Or
3) We should change the date of our flight ?
TQ.