If I was to fly to Auckland through Sydney with guns, is it a problem?

Probably depends on whether you intend just remaining in transit or if you want to get out and about in Sydney.
In transit usually does not present any issues so long as your Sydney - Auckland carrier approves the carriage of firearms (if this carrier is not the same as the one that brought you to Sydney).
If you want to stop over in Australia you will need import and export paperwork for your firearm.
This in itself is typically a paperwork formality.
We can direct you to the source of these formalities if the latter applies.
Who are you hunting in NZ with ?

Thanks. It is not finalized yet. I am thinking of going with Glenroy.

Better to fly direct Larry. Sydney is a little perculiar with O/S visitors guns at the moment; for people transiting to international flights or wanting to stop in on the way IN to the country. I am not sure they (NSW Govt) will even issue you a permit because transit isnt a reason to issue one. It is just an error that hasnt been corrected yet, it is no big deal for anyone coming in to Sydney to transit to other Au states as they will have all the AU papers for import.

If you have a connecting flight you should be fine as you probably wont enter the country with them - but if there is a problem with your connection it might be a hassle. The guys in Sydney Customs (the error is not their fault) are very easy to deal with though and if do go ahead on that route I can send you a contact who will help if there is any hassles.

Matt:

It didn't sound like a real good idea to me. Delta flew there and I am at their highest level in their frequent flyer program. I try to fly with them whenever possible. They don't fly to Auckland.

If I go, I will fly direct.