The following study introduces FT-QNN, a federated and quantum teleportation –based quantum neural network, utilized to optimize resource allocation for future wireless communications. The proposed FT-QNN consists of edge quantum neural networks (QNNs) and a cloud QNN, while quantum teleportation allows the cloud QNN to obtain the outputs of edge QNNs without requiring prior measurements on the output states, allowing the cloud to process the outputs directly as quantum states. As a particular case to demonstrate its applicability for wireless resource allocation, FT-QNN is then employed to optimize transmit power allocation coefficients in a power domain non-orthogonal multiple access (NOMA)-based system, aiming to maximize the achievable sum-rate. FT-QNN yields lower complexity compared to a distributed QNN scheme without quantum teleportation, while the numerical results also demonstrated that the FT-QNN is capable to achieve a similar sum-rate compared to the scheme without quantum teleportation.