I found this, it may help!
Kuwait Passport & Visa Requirements
Visa Agencies: Avoid the stress and queues, get a visa agency to arrange your visa.
Travel Visa Pro, San Francisco, USA. 1-888-470-8472 or www.TravelVisaPro.com
Global Visas, London, UK. 0207 190 3903 or www.globalvisas.com
Entry requirements for Australians: Australians must have a passport. A visa is available on arrival for up to three months.
I think this is the same as Bahrain and the rest of the Middle East, basically you can get a VISA of up to 3 months upon landing, but this does not allow you to take up employment! So far as I know, and this is true for everyone (having lived there for 2 years) that you only need a sponsor if you are going to work there, and the company undertakes the process of getting you a VISA from the government offices. But apart from that, you don't need a sponsor just for visiting! I did find that in Bahrain when I landed there was a charge of BD5 for VISA purposes, so I would check this, but I didn't have this in Dubai or Abu Dhabi! See note below....
Passport/Visa Note: All travellers must have documents and tickets for onward or return travel. Those requiring a visa may obtain one on arrival for a fee of up to 5 dinars, provided they hold sufficient funds to cover their intended stay. Visas may also be obtained prior to departure.
Note: Passport and visa requirements are liable to change at short notice. Travellers are advised to check their entry requirements with their embassy or consulate.