The law in Taiwan used to favor the father. The law has now been changed so that mother and father have equal chance for custody. There are still complaints that more conservative ministries like the Ministry of the Interior are still hindering single mothers. For example, your child will have her father’s surname. If you divorce, you will currently not be able to change the surname unless both parents agree.
If the divorcing parents do not agree in their agreement who should get custody, the courts will decide on the basis of the child’s best interest. This includes but is not limited to the child’s economic interests. Apparently the court will ask a social worker to visit the parents and child and the opinion of the social worker will carry a lot of weight. I would see this as a dangerous variable for you. If you are in Taipei, you may well get a more liberal social worker who is open to the idea of a foreign mother raising a Taiwanese child. Outside of Taipei, you might run into a more conservative one.
There is a famous case in Taiwan where the courts have awarded custody to an orphaned child’s Brazilian grandmother (the Taiwanese relatives have appealed), so the system is not necessarily stacked against you.
If you would like to get an opinion from an English speaking lawyer (who will charge you but will know of what she speaks), please PM me.