It's probably overkill. You could do this...

# SUBS

my $log = Log->new();

sub do_this{
    $log->log('Log This');
}

sub do_that{
    $log->log('Log That');
}
[download]

Or even this...

# SUBS

my $log;

sub do_this{
    ($log||=Log->new)->log('Log This');
}

sub do_that{
    ($log||=Log->new)->log('Log That');
}
[download]