In some applications, video content needs to be encoded and uploaded to a remote destination within a pre-defined amount of time. In order to guarantee that the overall processing time does not exceed certain time constraints, a system that performs joint encoding and uploading time control is needed. Such a system requires the flexibility to control both the time spent in the encoding process and the bit-rate. This is because the latter significantly influences the transmission time, especially for transmissions under low bandwidth constraints. This paper proposes a novel approach to address this challenge by adapting the Quantisation Parameters (QP) of a video encoder in order to meet overall processing time requirements, including both encoding and uploading time. The proposed QP adaptation approach relies on mechanisms to accurately predict the encoding time and bit-rate during the encoding process for the incoming group of pictures. This in turn allows adequate QP selections that result in accurately meeting the overall time constraints. A comprehensive experimental evaluation shows that the proposed QP adaptation approach can accurately meet the overall time constraints by efficiently adapting the encoding process to different target times and bandwidth conditions.