As 5G is offering new services that include improved security for its core functions, there is an effort to secure all domains in 5G, including control, data, and synchronization. This has turned the attention to 5G fronthaul communication security, which has not been considered crucial for past generations of cellular technologies. With overall information security efforts increasing preparation for the deployment of post-quantum cryptographic algorithms, there is also a need to assess the feasibility and overhead when such algorithms are considered for 5G Open Fronthaul communications between the radio heads in base stations and distributed units within the network. This is crucial for protocols such as eCPRI which has certain real-time requirements to meet. To this end, this paper first proposes an integrated security solution that combines IEEE 802.11AE (MACsec) along with a post-quantum-based EAP-TLS authentication within a typical ethernet-based fronthaul topology. We then implement a proof of concept to integrate all these components in a virtualized setting for the first time and evaluate the associated transmission delay with the eCPRI messages under various settings. The results demonstrate that MACsec can be a viable option that can satisfy the real-time requirements when used with post-quantum-based EAP-TLS1.3 that offers perfect forward secrecy.