While I have no experience with DNS::ZoneParse in particular, you can probably get a good idea of the structure of this hash using Data::Dumper. Once you have a dump of the datastructure, you can check perldsc to get hints on how to pull pieces from the hash. Hopefully this (overly) general advice will help you out some. :)

Update: looking at the docs for DNS::ZoneParse, it looks like soa() returns a pretty straightforward hash reference. Maybe some code like the following will give you an idea how to use it:

my $soa = $zonefile->soa();
print "serial:  ", $soa->{serial}, "\n",
      "origin:  ", $soa->{origin}, "\n",
      "primary: ", $soa->{primary}, "\n";
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Note: this is all untested code. I simply made an educated guess from the docs.