CBC-MAC: is it secure to authenticate a fixed length ciphertext?
Yes, if your encryption algorithm is reasonable secure.

Given fixed length messages (in your case the ciphertext), CBC-MAC is a secure MAC scheme, meaning that an attacker, without knowing the key, cannot produce a valid message-tag pair with non-negligible probability. Furthermore, according to this paper, Encrypt-then-MAC is the best procedure, while MAC-then-Encrypt and MAC-and-Encrypt are vulnerable to chosen-ciphertext attacks, the latter may even weaken the security of the encryption scheme itself. Thus the security of your system depends solely on the encryption algorithm you use. The ciphertexts it produces should be indistinguishable under chosen-plaintext attacks (IND-CPA). In other words, an attacker who sends two messages to an oracle and gets one ciphertext in return won't know which one of the two messages were encrypted.

AES in CBC mode with an initialization vector chosen randomly each time you encrypt a message is assumed to have this property.