I'm an Australian and have previously travelled to Iran; can I go to Guam without a visa?

This is only a partial answer, but it's too long for a comment.

There is a separate Guam-CNMI Visa Waiver Program that is open to citizens of certain countries, including Australia. ("CNMI" stands for Commonwealth of the Northern Mariana Islands.) There have been some proposed changes to this program under which applicants for this program will be asked, among other things, about their travel to several other countries (including Iran) since 2011. However, it does not appear that travelers who have visited these countries are completely barred from this program, as they are for the "main" Visa Waiver Program. It is also not clear to me whether these changes have taken effect yet, or when they will take effect.

You can see a more complete list of the proposed changes in the Federal Register.

The restriction on people having visited Iran only applies to the "main" Visa Waiver Program. You're entering under a separate arrangement called the Guam-CNMI Visa Waiver Program, and thus are not affected (and should not apply for an ESTA).

TIMATIC, the database used by airlines, states the following regarding mainland US (for entry under the VWP):

Detailed information on ESTA restrictions can be found on https://www.cbp.gov/travel/international-visitors/esta#

It should say "VWP restrictions", but, in any case, no reference to this is made when Guam is selected as the destination. Nor does the DHS page about the Guam-CNI VWP mention it at all.

That said, in order to reduce the amount of paperwork to fill out on arrival, you should register here up to 7 days in advance of your arrival, and present a printed confirmation on arrival

Timatic has this to say about visa exemptions for Australian travellers to Guam:

Nationals of Australia, Brunei Darussalam, Japan, Korea (Rep.), Malaysia, Nauru, New Zealand, Papua New Guinea, Russian Fed. and Singapore traveling as tourists or on business under the Guam-Northern Mariana Isl. Visa Waiver program for a maximum stay of 45 days. They must have :

• a machine readable passport, and
• a signed Form I-94 (05/08), and
• a signed Form I-736, and
• a return/onward ticket to a country other than the USA or than the neighboring islands of Guam. This does not apply to residents of the USA or of the neighboring islands of Guam who can have a return/onward ticket to the USA or to the neighboring islands of Guam.

Though I must admit I am not sure what they mean about a signed I-94. That bit doesn't make sense.