How do I call a 6-digit Australian phone number with a US-based mobile phone?

13xxxx is a "magic" number.

For instance, calling 131 888 will ring the nearest Domino's Pizza (to your location in Australia). Your number will presumably reach the nearest Kia dealer.

From Wikipedia:

13 xx xx, 1300 xxx xxx and 1800 xxx xxx numbers can provide source-based routing, used by organisations such as pizza chains that advertise one number nationwide that connects customers to their nearest store.

These magic numbers do not work internationally, for obvious reasons.

To dial a number in another country, you first dial the international access code for your country, then the code for the country you're calling, then the actual phone number, usually omitting the first zero if any.
You can replace the international access code with a + on mobile phones.

The international access code for the US is 011.
The country code for Australia is 61.

So that would make it 011 61 131542 or +61 131542 for your example.

However, that may not work. The Australian equivalents of the US 1-800 numbers are 13 numbers (as well as 1300 and 1800), as is the number you want to call. They are charged at a local rate to the caller. The downside is that they're often not available from abroad, likely because the owner is charged the actual cost of calling the number.

However, Kia has a dealer locator that shows phone numbers for those dealers. Those seem to be regular phone numbers that are callable from outside Australia. Pick one of those and call them, either doing your business with them directly, or asking them for a number to call from abroad.

Alternatively, you can call Kia USA and ask them for a number to call Kia AU on.

They aren't accessible from every country, but from the US it should be.

[International dial-out code] + (61) + your inbound number should do the trick.

So in this case, 1100, if that's your dial out code, 61, then 131542.

Note: + usually means international too, replacing 00, so in my experience I just dial +61 131542.

I'm not sure about the dial out code, you'll need to see if you need that (I don't from NZ), but as I'm in NZ at present I just tried, and dialling +61131542 worked for me.

Telephoning Kia from International may not be possible because of their short number - it may be a special number like a US 1-800 that doesn't work internationally.

Australian landline telephone numbers are 8 digit.

Australia uses eight digit local phone numbers preceded by a two digit STD area code.
Source

So the quoted 6 digit phone number is something odd.

The Australian country code is 61. When calling from outside Australia, leave out the leading '0' from the STD area code or from the mobile telephone number.

Example: Fixed line example calling Canberra from outside Australia: +61 2 (local eight digit number)

The Area Code for NSW is probably 02 but some areas may use the 08 and 03 area codes instead.
Source

Alternatives, why not use a simple local telephone? Payphones still exist, or your accommodation should have some kind of telephone. You could also purchase a "prepay" or "pay as you go" sim and see if it works in your phone. Or purchase a cheap cellphone for the time you're in Australia, and gift it to someone else before you leave.

One approach that is generally useful for calling toll-free numbers (from outside the country they're intended to be used in) but, unfortunately, fails in the case of Australian toll-free numbers is to use Skype to phone (you need to have a credit to use the service, about $10 USD is the minimum):

Yes, use the dial pad to enter toll free numbers on Skype. The following countries and number ranges are supported and are free of charge to all users:

France: +33 800, +33 805, +33 809

Poland: +48 800

UK: +44 500, +44 800, +44 808

USA: +1 800, +1 866, +1 877, +1 888

Taiwan: +886 80

That also allows you to call regular phones from a cell phone using local cellular data or WiFi access points, which I find very useful. Again, it's not free, but quite cheap (2-3 cents/minute), in my experience.

It is not enough to use 61 as the country code.

You must also use an area code.

So +61 2 132221 for CBA IVR/VRU

Be aware that 13 numbers are not always the same across all area codes or even regions that share the area codes. Annoying if it is used in a jingle and then does not work.

If you are calling Centrelink (!) be very sure to tell them where they might think you normally live, their systems may make assumptions and not find your records, the same as calling them from interstate.

This is a big problem between SA and WA as they are both '08' or +618. You will likely get the SA number. You cannot dial 1194 in this way, and inside Australia 081194 is the time in Adelaide, not Perth.

Be also aware that most companies using 13 numbers have an alias landline number specifically for calling from overseas.

SQB covered it very well.. Six digit 13 numbers are generally for use only within Australia because the owner of the number might be charged for its use. That is also why there are significantly higher call rates for those numbers on Skype if you can get them to work.

To call Australia landline numbers use either 001161 or +61 prior to the Australian number. Landlines will have a two digit area code beginning with zero (0) and mobile numbers all begin with 04. In both cases drop the zero. For example landline 02-12345678 becomes +61212345678 and mobile 0412345678 becomes +61412345678.