There is no handling fee for Taobao to pay by credit card, but there is a limit for payment. According to different regulations of different banks, you can have a look at it when you pay. If the limit is exceeded, you will not be allowed to pay.
Taobao supports credit card payment, but not every store can. When searching for baby, you can check the "credit card payment" under the search box. Generally, there will be a logo similar to a credit card under the baby. Taobao credit card payment is free.
If you are not sure, you can call customer service for detailed consultation, or you can ask Taobao sellers whether it is necessary to deduct the handling fee when paying by credit card.