At reception, you can order bread for breakfast, and buy gas cylinders, ice-cream and other small things.
There are plenty of places to shop near Køge & Vallø Camping. The campsite has a Statoil right next-door, with a kiosk which is open every day until 22:00. Less than 800 metres from the campsite is a large Netto, which is likewise open till 22:00 daily. And walking just half a kilometre gets you to Køge town centre, with loads of shops.