Ciphers are deterministic. As such there is no such thing as "ciphertext entropy". Given a certain key, IV, and plaintext you should always get the same ciphertext. If neither of those elements contains entropy then no entropy is in the ciphertext; it may look randomized but that's not the same thing.
AES by itself is not a generic cipher, it is a block cipher and considered a primitive. A primitive can be used to build generic ciphers and other cryptographic functions. A generic cipher should be able to encrypt arbitrary messages up to a certain size. It should at least be IND-CPA, indistinguishable under the chosen plaintext. As the block cipher itself only encrypts blocks (ECB) it is not considered to be IND-CPA; if the attacker guesses the correct message then the oracle will provide the same ciphertext, making it distinguishable.
Say that we have a cipher such as that provided by AES in a secure mode of operation or the ChaCha20 stream cipher scheme. In that case, it may retain the entropy provided in the key and - to a lesser extend - the IV. However, it would be hard to say how much is retained. If you use a keyed cipher to encrypt a single bit then obviously most of the entropy is lost.
In general, there is no real way to measure entropy if it may have passed through a pseudo random function. There are ways to see if a large amount of ciphertext is indistinguishable from random. For that, you can see e.g. the die-harder tests. But those tests cannot distinguish pseudo random sequences from true random sequences and are unsuitable to test for entropy for that reason alone. You could these tools on a known entropy source to estimate the amount of entropy - but a cipher is not an entropy source.
There is a lot of discussion on this site on what entropy actually is. There are several definitions such as Shannon entropy and min-entropy. I'd say that this is an advanced subject that may not be that suitable for a school project.