There won't be any special service to expedite your movements through the airport, apart from the short connections lane at passport control.

If the KLM computer thinks you will miss the connection you will most likely be automatically rebooked shortly before landing in AMS. If you disagree and think you can make it anyway feel free to run to the gate - if you make it there is a good chance to be put back on. If an overnight is required you won't get a hotel assigned automatically. Either go to a transfer desk to get one, or book something yourself and get it reimbursed later.

Don't worry too much - 45 minutes is not a lot, but certainly enough if the CPH flight is on time.