my $paused :shared = 0;

sub thread {
    while( my $domain = $queue->dequeue ) {
         sleep 1 while $paused;
         ## the rest of the thread code.
    }
}


...

$pauseButton->onclick( 
    sub {
        if( $paused ) {
            $paused = 0;
            $self->settext( "Pause" );
        }
        else {
            $paused = 1;
            $self->settext( "resume" );
        }
    }
};
...