Quantum networks connect devices to facilitate the transmission of quantum bits (qubits), harnessing quantum mechanics for groundbreaking telecommunications applications. The quantum state exchange rely on quantum entangled particles which have to be sent from a Quantum Base Station (QBS) to Quantum Nodes (QNs) through an optical channel. Free Space Optical (FSO) links promise flexibility and cost advantages over the classical fiber-based infrastructure. However, the absence of Line of Sight (LoS) between the QBS and QNs may completely disrupt the communication. Therefore, this work focuses on an Intelligent Reflective Surface (IRS)-assisted Unmanned Aerial Vehicle (UAV)-aided FSO quantum network, modeled considering drone kinematics and optical channel dynamics. An optimization problem is formulated to fairly maximize qubit reception at QNs by optimizing UAV trajectories, speeds, and accelerations, constrained by fidelity and link-per-IRS limits. The intractability of the original formulation is tackled with a dedicated strategy which combines sigmoid-based approximations, Block Coordinate Descent (BCD), and Successive Convex Approximation (SCA) techniques to achieve a quasi-optimal solution. Numerical results (i) validate the approximation accuracy, (ii) compare the effectiveness of the proposal against a baseline approach under varying conditions, and (iii) show the interplay among the degrees of freedom and the relation with the scenario parameters.