"ping zaphod" without "daheim.local" is working! If I "ping localhost" the reply is "zaphod" not "zaphod.daheim.local".
But does it realy matter? I think, if I (like i did) query a DNS server via NSLOOKUP and the resolver answers with "…Non-existent domain", it should not be a problem of the client machine?!
Is there a way to look into the table, where the DNS server holds its entrys? I found nothing in the status or diagnostic page or status.php.