Quantum computing has redefined the assumed complexity of different computational tasks, which implies the need for new cryptographic tools that can be considered secure even in the presence of entities that may be able to execute quantum algorithms. In particular, this poses significant challenges for the adaptation of cryptographic implementations, which are particularly relevant in the IoT scenario, where resources are especially limited. In this work, we report on a simple cryptographic protocol for group key establishment, where n > 2 devices interact to establish a key to secure their communication. Our design can actually be seen as a so-called key transport, where a small set of devices cooperatively choose a key that is subsequently distributed to all users over an insecure (and somewhat unstable) network using only cryptographic tools that are claimed to be post-quantum, i.e., resistant to quantum attacks. We give a theoretical description and also describe our experimental results implementing our protocol within networks up to 16 nodes based on ARM Cortex-M4. We believe that this design is a first proof-of-concept of a post-quantum group key exchange protocol in the IoT scenario.