Realistic quantum systems are the main part of quantum information technology, which causes the rapid destruction of crucial quantum properties. Therefore, the unavoidable interaction between quantum systems, understanding the dynamics of entanglement indicators and finding the correlation between different phenomena may stimulate great interest. In this article the quantum Fisher information and nonlocal correlation between a single qubit and two-mode optical field initially in pair coherent states have investigated. We examine the impact of the qubit motion and intensity dependent function on the flow of quantum Fisher information and quantum entanglement during the time evolution. We discuss the relationship between quantum Fisher information flow and quantum entanglement in the case of moving and unmoving single qubit.