The Ultra-Dense LEO Satellite Networks (UDLSN) has immense potential to provide low-latency and high-reliability services in future communication networks, owing to its global coverage, high capacity and reliable connectivity. However, the LEO networks usually suffer relatively high and variable transmission errors due to multipath, shadowing and handover. For delay-constrained video transmission, existing packet protection mechanisms frequently violate the constraint and degrade quality in such environments. In this paper, we propose a QUIC-Enabled Reliable Video Transmission Scheme (QRVTS) with adaptive Forward Error Correction (FEC) to reduce loss recovery time and enhance transmission performance especially for delay-constrained videos. Specifically, QRVTS incorporates an adaptive mechanism to dynamically adjust FEC redundancy based on the prevailing channel loss conditions and frame types. We evaluate our mechanism under multiple satellite scenarios with different network characteristics. The simulation shows significant gains in overview completion time and frame-level delivery delay for delay-constrained video transmission in LEO satellite scenarios.