Leveraging broad frequency ranges, as they are available in the terahertz (THz) regime, for high-bandwidth communications makes the energy consumption of the receiver's analog-to-digital converter (ADC) a major challenge. To solve this problem, a promising approach is the use of ADCs with 1-bit amplitude resolution in combination with temporal oversampling. This coarse quantization, however, necessitates the redesign of most receiver algorithms. This work addresses the estimation and compensation of in-phase and quadrature (IQ) imbalance, a critical factor regarding the communication performance. It is shown that amplitude imbalance has no deteriorating effect on the communication performance, while the impact of phase imbalance is significant. To address this, an efficient unbiased estimator for IQ phase imbalance based on 1-bit quantized observations is derived, achieving the Cramér-Rao lower bound (CRLB). Its accuracy, its robustness against inaccurate timing conditions, and its performance gains in case of oversampling are assessed. Furthermore, a guideline is derived, which either recommends or discourages compensation with regard to the expected variance of an individual estimate. Thereafter, this work discusses approaches to carry out the compensation of the estimated IQ imbalance. Eventually, simulations reveal the estimator's ability to significantly enhance communication performance.