Doctors' surgeries all open at round about the same time. If you take a prescription there straight from the surgery, there is likely to be a bit of a queue of other people who have come from your surgery and possibly some others. Take it along a couple of hours later and you probably won't have to wait long at all.
Also, bear in mind that a chemist's job is full of risks. They will check constantly that you are being given the right product, at the right strength and with the right dosage instructions printed on it. I for one would rather wait 20 - 30 minutes and know it's right, rather than accept something from somebody who's stressed and hurrying and may make a mistake.