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URGENT replies please - connecting PVC downpipe in carport to existing downpipe

We are about to sell our house but the sale of the house is on the condition of joining the downpipe in the carport to the storm water system. We would need the guttering to extend along another side of the carport (turning 90 degrees) and then connect up to another downpipe that is approximately 3m away that runs down the side of the brick of the house (this will make sense when you view it). The most important thing we need to know is WHEN you can do the work - the sooner the better and we need certainty from you given that we are dealing with a deadline of settlement of our house. We also need to know costs obviously. See pics below attached for more detail. Thank you :)