Quantum-Dot Cellular Automata (QCA) is a candidate alternative technology for CMOS technology in VLSI circuits in the post-transistor era. QCA can be implemented in molecular and nanoscale structures. In VLSI circuits, the Arithmetic and Logic Unit (ALU) is one of the most critical units, which is an optimal design with low latency is essential for better processing speed. In this paper, an ALU is designed based on the needs of the one-dimensional clock. The proposed ALU has only 1.5 clock cycles latency, supports 12 instructions, and uses 443 cells in three layers. In addition, all inputs and outputs are in the same layer to make connecting the proposed ALU to other blocks simpler. To achieve this latency and the one-dimensional clock capability, AND, OR, XOR gates are fully redesigned to work in the one-dimensional clock structure. The one-dimensional clock enables the design of the clock bed and QCABED separately. Besides the proposed ALU in this paper, design rules are also proposed for one-dimensional clock circuit designing. Proposed designs are confirmed by QCADesigner, a well-known QCA layout design, and verification tool. QCADesigner-E was used for power estimation.