What is your favorite Australian food? My favorite American food is Kung Pao Chicken. No, really, my favorite American food is Reeces Peanut Butter Cups.

Peanut butter cakes - are they like a peanut butter flavoured cup cake or mega size one as we now have called muffins?

You'll find as far as favourite foods go, Oz is very diverse, and it really depends on personal taste but we have plenty of Asian and Indian restaurants, less of middle east and meditteranean but still plenty of Italian.
Capital cities and most population being on or near coasts, seafood of all descriptions is as popular as beef/lamb/pork/chicken dishes, all of which are available in Asian/Indian/Med/ME styles/flavours.

Aussies like a weekend BBQ and it can be as simple as a few snags in a slice of bread right thru to cordon bleu quality, washed down with beers or wine if an alcohol is desired.
Takeaway is as big as the states and apart from the Maccas/Pizza Hut/Colonel Sanders and all the like brands, again asian and indian takeaway is available and the best of all Friday Night fish and chips, Sydney also having a huge fish market.
For the best fish and chips however, you need to find a shop that has flake (yes shark like in JAWS), not so widely available in NSW but more so in Vic and some Queensland locations, or go to Queensland where a great variety of reef fish is more widely available at the fish and chip shops.
Sydney and more touristy areas is also expensive re fish and chips and food generally and so take some weekend drives to coastal towns further afield.

Deserts are also quite diverse with all manner of cheese cakes and other Gateaus and though not something that you will find often in a restaurant, if doing a trip Vic way, do it in February/March and find someone who has blackberries about and a freshly baked blackberry pie is something else!
Oh, and I also understand from other Anericans that most would not be familiar with a passionfruit! - whilst in Australia, do take a trip north to Queensland to sample no end of fresh tropical fruit - actually Tropical Fruitworld is just south of Queensland/NSW border and yes, even Strawberries in winter - probably also tucked to Sydney markets.

You may well find Oz is a foodies paradise and also not too badly done by with wines too.

Peanut Butter Cups are a candy, chocolate wrapped around peanut butter, and the small ones are shaped like little cups. For some reason they are hardly available at all outside the US and Canada.

I was interested in food that is local to Australia, or at least started out that way. I've heard of something called damper, which I think is some sort of bread made over an open fire, or when camping out, or something.

You've about got it in one and mod cons have produced variations, hence a camp oven recipe - http://www.abc.net.au/northtas/stories/s512810.htm

But traditional bushman's way was to wrap mixture around a green stick (so stick would not burn)
One source of the word damper is thought to be that it is best to use a damped (not wetted, but more just coals) fire for slower controlled baking, and that certainly helps to keep the hands from being cooked if you have not got too long a stick.
Another method that can be used is to wrap a lump of mixture in foil, place in a formed hollow of coals and cover over with hot coals.

Other camp fire favourites are putting potatoes in the coals and then cut in half and put butter on, using a spoon to scallop out leaving the charcoal skin.

Marshmellows on a stick toasted lightly before they melt.

Chocolate bananas - just slit banana skin on one side, sufficiently to remove banana and then put in shredded/chips of chocolate along with the banana, wrap in foil or a banana leaf or similar if you had one and leave under coals a few minutes before eating out of skin.

What else is really Australian?

Well, there's vegemite. Not my favorite, but some people carry it with them when they leave the country because they can't do without it.

Pavlovas. That's a cake named after the Russian ballerina. A picture and some history.

There's Anzac bikkies(cookies) and apparently according to forum linked, Apple Crumble is an aussie thing as is use of pineapple in curries.

Forum - http://www.vegsoc.org.au/forum_messa...330&Topic_ID=1 and then there's always the Sunday Lamb Roast that probably does not occur all that often these days, and there's a Ploughman's Platter listed along with a few other platters on Regatta Hotel Menu - http://www.regattahotel.com.au/funct..._platters.html

You'll even find that in common with the Irish influence in America, there is a great liking for stews here in winter in colder areas, and depending on the cook and how adventurous they may want to be, dishes like stews and curries can be spiced up to suit - many Aussies have an "Anything goes - she'll be alright mate" attitude that can even be taken to meals - and often the hotchpotch could well be determined from the last couple of days leftovers.

Tim tams, pie floater, vegemite, kangaroo, emu, aussie pizza