Coolangatta is right at the southern end of the Gold Coast. The touristy things are mostly at the northern end of the coast, at and near Surfers Paradise and Broadbeach, about 20 or so miles north of OOL airport (20 to 40 minutes depending on time of day and time of year). So if you do go, plan on transport north to where the action is.
However, if you are just wanting a nice beach to swim and soak up some Queensland sunshine, then there are plenty of beaches and accommodation closer to the airport, a cheap taxi ride away. If staying overnight, there are lots of great places to eat and all sorts of entertainment. But unless you are staying in Surfers Paradise, you will probably need transport.
OOL is only an hour flying time from SYD, as in BNE. BNE and OOL are similar time from Surfers Paradise, though OOL is less distance.
Its a pitty you don't have more time, since there are lots of things to see and do on and around the Gold Coast, so choosing what to do in a single day will be hard, and will depend on what you enjoy doing most (shopping, lazing on a beach, theme parks, bush walks, nature reserves, etc).
Again, depending on what you like to do, consider visiting
Currumbin Wildlife Sanctuary, which is only about 10 mins drive north of OOL and very near the beach.