Quantum physics in the Copenhagen interpretation places a divide between the quantum and classical worlds. Decoherence — the destruction of superposition states of the system — underpins our understanding of the quantum-to-classical transition. Quantum Darwinism builds on decoherence to understand how information about the system is deposited in the environment. This gives a framework to describe the emergence of objective, classical reality from the fundamentally unpredictable quantum world. Considering a model of a qubit interacting with a symmetric spin environment, we study how information about the system is transferred into the environment when the system has intrinsic dynamics. That is, we examine a model beyond pure decoherence. We develop a computational technique to compute the mutual information between the system and a fragment of the environment as a function of the strength of the system’s Hamiltonian. The intrinsic dynamics of the system influences the proliferation of information. However, there is always a redundant transfer of information for a weak system Hamiltonian. Only when the system evolves so rapidly that environment can not effectively monitor its state does redundancy vanish.