Would a Jewellery store set my pearl into a brooch for me?

Yes.jewelers are your best bet because pearls are very delicate. If your mother has a brooch she loves,go to the jeweler to add the pearl so that it's set properly, and If you can buy a gold setting, it would be better than silver as silver tarnishes. And in the future for cleaning I'd bring it to a jeweler as you can damage the pearl with either home remedies or over the counter products. There are pearl settings with just one pearl in gold and looks very pretty as a necklace. The cost varies depending on how heavy or light the setting is. A lovely birthday gift indeed. You're a thoughtful and wonderful son to give your mom something from you that she'll cherish always.Peace.