We consider a system in which two nodes take correlated measurements of a random source with time-varying and unknown statistics. The observations of the source at the first node are to be losslessly replicated with a given probability of outage at the second node, which receives data from the first node over a constant-rate channel. We develop a system and associated strategies for joint distributed source coding (encoding and decoding) and transmission control in order to achieve low end-to-end delay. Slepian-Wolf coding in its traditional form cannot be applied in our scenario, since the encoder requires the joint statistics of the observations and the associated decoding delay is very high. We analytically evaluate the performance of our strategies and show that the delay achieved by them are order optimal, as the conditional entropy of the source approaches to the channel rate. We also evaluate the performance of our algorithms based on real-world experiments using two cameras recording videos of a scene at different angles. Having realized our schemes, we demonstrated that, even with a very low-complexity quantizer, a compression ratio of approximately 50% is achievable for lossless replication at the decoder, at an average delay of a few seconds.