We construct a toy model of a nucleon, in which three static quarks interact via a SU(3) gauge field on a planar honeycomb lattice. The dynamics of the gauge field is described by the Kogut-Susskind Hamiltonian, truncated to the lowest three SU(3) irreducible representations. We show that the internal structure of the toy nucleon reflects salient features of the physical nucleon state. We then find the entanglement entropy of the gauge field within the nucleon state and compute its time evolution after a quench, in which all three valence quarks are suddenly removed. We show that the entanglement entropy in the final state is dominated by the dynamically generated contribution rather than that in the initial state.