You're using $xml as a scalar element, but exists requires a hash or array element. Also, remember to declare all of your variables. You forgot to declare $image. Here's the way that I would do it:

#!/usr/bin/perl

use strict;
use warnings;
use XML::Simple;
use Data::Dumper::Concise;

my %xml;
my $image;

my $web = 'http://my-base-url/';
if(exists $xml{'result'}{'covers'}{1}{'content'}) {
       print Dumper($image = "$web$xml{'result'}{'covers'}{1}{'content
+'}");
}
else {
    print Dumper($image = "$web$xml{'result'}{'covers'}");
}
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