I would like to recommend a little book called, "But you kill ants" by John Waddell.
http://crueltyfreeshop.com.au/index.php?main_page=product_info&products_id=197
It's a really easy read and ready reference. I actually carry it around in my handbag! It gives great answers to all the crazy questions vegetarians and vegans have to face.
I wonder if taking the conversation further on the topic of why she believes animals are here to serve us would be useful. Quite often people use the argument that animals are less intelligent than us. It might be worth just asking the question out of curiosity, without intention of rebutting it, then bring her answer back to us here and we can help with rebuttals.
Because you're friend says "there are two sides to every story," perhaps you could propose a fair deal. Maybe you could suggest that you will read/watch a piece of evidence of "her side of the story," if she would be willing to read/watch a piece of evidence supporting "your side of the story." Be prepared with references so you can back up everything you tell her. I wonder if she can back up what she believes with evidence.
She says she knows people who work on farms, so ask her, "what happens to all the calves born to dairy cows, esp. what happens to the male calves born on these farms? Are they allowed to stay with their mothers until natural weaning occurs?" "what happens to the dairy cows once they have passed their peak milk production but still have plenty of their life ahead of them, are they retired to live out their days in sanctuary?" For beef cattle, ask her, "how are the cattle transported to the abbatoir, and how are they killed, do the workers treat them with care and make sure they don't suffer? How do they ensure this when the cows waiting in line are watching the fate of the cows ahead of them?" "Do you know any pig farmers and how are the pigs housed?" "Do you know any chicken/egg farmers and how are their chickens housed?" I just wonder if this approach of asking questions that directly address the issues, rather than telling her how it is might help. That way you are seen to be expressing an interest in wanting her to share her knowledge. If you feel brave enough, perhaps you could ask her to arrange a visit to one of the farms of people she knows. BTW, does she really think farmers would admit that they are treating their animals cruelly??
With regards to the, "but that's in America, it doesn't mean it happens in Australia argument," see if you can get her to read/watch any of the following:
60 Minutes expose of conditions of pigs kept in Australian farms:
http://www.animalsaustralia.org/features/60-minutes-the-hidden-truth.php
Evidence used to convict pig farmer Gary Oliver in Tasmania:
http://www.youtube.com/watch?v=lpIrB6UOL7s
Investigation into Australian Chicken Meat Suppliers:
http://www.animalsaustralia.org/media/videos.php?vid=broiler-investigation
The facts about Australian Dairy Farming:
http://www.animalsaustralia.org/take_action/dairy/
Further down on this page is a stat dec from a former dairy farm worker:
http://www.alv.org.au/storyarchive/0832dairycruelty/dairy.php
And various videos here:
http://animal-lib.org.au/subjects/multimedia.html
I'm sure everyone else could offer heaps more links.
To the "the cows are happy" argument, does anyone know of any video evidence of the mother cows and calves distressed over their separation?
To the question, "why should I pay extra for eggs?" you could be a smart arse and tell her she doesn't have to pay more, she could just not eat them!!

A serious answer to this one is that you don't put a price on preventing the suffering of any being.
"The cows would die out," oh puleeeeese!!! As others have said, I reckon they would rather be extinct than endure the lives they do. Ask her, if she and her family were being bred and forced to endure lives of suffering for the benefit of another species, would she really prefer for that to continue indefinately than for the species not to be here at all. Actually, don't bother with that one, in my experience only veg*ns are capable of identifying with this argument.
With regards to the environmental issues offer info from very reputable sources such as the United Nations:
http://www.fao.org/docrep/010/a0701e/a0701e00.HTM
And this is a good brochure:
http://dl.dropbox.com/u/4021380/So%20You%20Think%20You%20Can%20Be%20A%20Meat%20Eating%20Environmentalist.pdf
Nearly there!
When you are told you are just "joining the craze" of being vegan, just say, "We'll see!" and know in your own heart that you will stay true to your convictions and time will prove them wrong. Not that I advocate gambling, but the shock factor is always fun when you offer them a bet that you will still be vegan in ten years time!!!! When I was 25, a friend didn't believe me when I told them I was never going to have children, so she suggested a bet with me that I would have a child by the time I was 35. I'm looking to collect in November!!
And the teasing about being "Mother Teresa" or a hippy. Take that as a compliment and tell them so. What a wonderful person was Mother Teresa. Who wouldn't want to be compared to her in terms of love and compassion.
Finally, if you're feeling lonely and victimised, come in here frequently, it's done wonders for me.