A man and woman who allegedly led police on a pursuit through a series of Gold Coast suburbs in a stolen car, before dumping the car and running through a number of residential properties, will face Southport Magistrates Court on Tuesday.

Police will allege the pair, a 24-year-old man from Nerang and a Springwood woman, 19, stole the car from Mermaid Waters before repeatedly evading officers attempting to intercept them.

The police helicopter monitored the pair from the air as they allegedly ran from police on the ground.

They were arrested in Palm Beach after dumping the car and fleeing on foot.

Each has been charged with entering a premises with intent to commit indictable offence, unlawful use of a car and dangerous driving.

The woman faces a second charge of entering a premises with intent to commit indictable offence, along with further charges including stealing, failing to stop, unlicensed driving, possession of a knife and possession of a laster pointer.

The man also faces a further charge of driving while disqualified.

In a separate incident in Windaroo, near Beenleigh, later on Monday, two men allegedly held up a convenience store, one armed with a gun and the other a golf club.

The pair were charged after allegedly entering the Beenleigh-Beaudesert Road store just after 8pm and demanding cash and cigarettes from the console operator.

The console operator complied and the men fled. Police arrested them nearby a short time later.

A 17-year-old Mount Warren Park man and a 21-year-old Meadowbrook have each been charged with armed robbery in company.

Both men are scheduled to appear in the Beenleigh Magistrates Court on Tuesday.

In a third incident, just after 10pm in the Gold Coast suburb of Nerang, an 18-year-old man was charged with wilful damage, after allegedly using a hammer to smash three windows at a Spencer Road service station.

He is scheduled to face Southport Magistrates Court on April 22.