Can anyone tell me if my husband and I need to get a notarized birth certificate and authentication from the Ministry of Foreign Affairs when taking our 5-year-old child to the Czech Republic ?

Of course, it is necessary.

Remember if both parents travel together and the hukou is in the same book, you don't need it! If they are not in the same book, you need it, but it is not necessary. My friend got his visa last month even though his hukou was not in the same book.