If you are entering through Sydney and New South Wales, check out these websites for more information:

http://www.police.nsw.gov.au/about_us/structure/corporate_services/firearms/more_information/licences,_permits__and__registrations/permits

How to Apply for a Firearms Permit

Application Forms

Permit application forms are available by phoning the Firearms Registry Customer Service Line on 1300 362 562.

Supplementary Instructions are available for the following types of permits:

Ammunition - Collectors Permit
etc
....
Overseas Visitors Permit - Safari Tour Hunting Activities
Overseas Visitors Permit - Target Shooting Competitions
....
Permit to Purchase a Non-Prohibited Firearm on Leaving Australia
....

You can view the Supplementary Instructions for each of these permits on the 'Forms, Brochures and Permit Instructions' web page.

http://www.police.nsw.gov.au/about_us/structure/corporate_services/firearms/more_information/forms,_brochures__and__permit_instructions

http://www.police.nsw.gov.au/about_us/structure/corporate_services/firearms/more_information/forms,_brochures__and__permit_instructions/permit_instructions/permit/overseas_visitors_permit_-_safari_tour_hunting_activities

Supplementary Instructions for a
OVERSEAS VISITORS SAFARI TOUR/HUNTING PERMIT
The following information and instructions should be read in conjunction with the general instructions on the Application for a Permit under the Firearms Act, 1996.

Instructions to all applicants
These instructions are specific to the type of permit for which you are applying. You must ensure all the requested information is provided at least 28 days prior to your arrival in NSW or the application will not be able to be processed.

This permit only authorises participation in activities conducted by an authorised safari tour operator or in hunting activities conducted by an approved hunting club. This permit will authorise the possession and use of category A or category B firearms only . The permit does not authorise the purchase of firearms.

The permit will be issued from one day prior to your arrival in NSW until one day after your departure from NSW. If you intend to travel further around Australia and hunt outside of NSW, please note that you will require a permit from each State / Territory in which you will be hunting.

If the permit is approved, a B709A Certificate will also be issued to allow the release of firearms and ammunition from Customs upon arrival in Australia.
Applicant Requirements
Completed permit application form P568.
Proof of Identity: Provide a copy of your passport.
Provide details of:
Your date of arrival in and departure from NSW (If you are travelling to other States / Territories but do not wish to hunt there, please advise the dates of your arrival / departure from Australia. The permit can be issued to include authority to carry the firearms in other States / Territories for transportation purposes only – HOWEVER, YOU MUST ENSURE THAT THIS IS ACCEPTABLE TO THE FIREARM AUTHORITIES IN THOSE STATES / TERRITORIES);
The name and permit number of the safari tour operator; OR
The name and approval number of the hunting club;
The location of the proposed hunting activities if known;
The period over which the hunting activities will be conducted.
Provide documentary evidence of the authority under the law of your country of residence to possess and use firearms to which a category A or B licence applies.
Provide a description of the firearm/s being used i.e.:
Make;
Model;
Serial number;
Calibre;
Firearm type.
Number or rounds and calibre of ammunition to be imported.
Provide the fee (See fee schedule.):
cheque or money order in Australian currency payable to the ‘Firearms Registry’, OR
if paying by credit card (NOTE: Bankcard, Visa, Mastercard Only) provide card number and expiry date, card holder’s name and written authorisation to debit Aus$75 to that credit card, signed by the card holder.
If you require any further information or need assistance in completing this application contact the Firearms Registry’s Customer Service Line on:

Within NSW: Tel: 1300-362-562 (cost of a local call)
From interstate: Tel: 02-6670-8590
From overseas: Tel: 61-2-6670-8523
Fax: 61-2-6670-8550
Email: firearmsregistry@police.nsw.gov.au

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[1] Category A firearms: air rifles, rimfire rifles (other than self-loading); shotguns (other than pump action or self-loading); shotgun/rimfire combinations.

Category B firearms: muzzle-loading firearms (other than pistols); centre-fire rifles (other than self-loading); shotgun/centrefire rifle combinations.