Artificial learners often behave differently from human learners in the context of neural agent-based simulations of language emergence and change. A common explanation is the lack of appropriate cognitive biases in these learners. However, it has also been proposed that more naturalistic settings of language learning and use could lead to more human-like results. We investigate this latter account, focusing on the word-order/case-marking trade-off, a widely attested language universal that has proven particularly hard to simulate. We propose a new Neural-agent Language Learning and Communication framework (NeLLCom) where pairs of speaking and listening agents first learn a miniature language via supervised learning, and then optimize it for communication via reinforcement learning. Following closely the setup of earlier human experiments, we succeed in replicating the trade-off with the new framework without hard-coding specific biases in the agents. We see this as an essential step towards the investigation of language universals with neural learners.