Hi laura,
First of all you have absolutely nothing to worry about!!! You are going to have the time of your life and when it's over you will laugh that you ever worried about it before you left. Saying that, it is completely natural to feel scared because i was really worried just before i left at Christmas and was convinced i would meet nobody.
Australia was the second country i visited and i had no problems and i can't think of a single day there that i spent alone.
I do think that 3 months in the east coast is a little too long as there are so many gorgous places you'll be missing out on if you do just concentrate on that area.
I was in Australia for 2 months and had planned just to do the east coast, but i changed my mind when i arrrived.
Instead i arrived in Melbourne and spent a week there, i travelled along the gt.ocean road to Adelaide then flew by internal flight (
www.jetblue.com.au) to Alice springs and did a one day trip to Uluru (a must see!!) then i flew to Perth by Quantas (wwwquantas.com.au) spent some time in Perth then flew to Sydney and travelled up the east coast to Cairns.
This was all in two months and although it sounds a lot and was i never felt rushed and had a fantastic time. You can get great bargains on seats on internal flights and they have a special time during the day when they reduce loads of seats i think it was 1pm-2pm but don't quote me on that!!
I spent £2200 on the whole trip acc, food, sight seeing, transport etc. And although i was being careful i didnt really really scrimp.
Greyhound was great especially as there are several buses a day as opposed to oz where there only one and sometimes only every couple of days. also on Greyhound you can travel overnight and save on accomodation. Some of the journeys are huge for such a little distance on the map!!!!
You will meet people as soon as you get to hostels especially i found in dorm rooms when you're making your bed or just come in with your bag, You'll get fed up of the same questions 'where have you come from? where you headed? how long have you been out for?' etc etc but it is all part of the meeting people!
Seriously you are going to have the best time, i did it as a gap year and now have uni to go to and am so glad i went out there and saw some of the world because i had the time of my life
Oh and no don't need any funds to show when you arrive if you're not working. The customs people were a bit arsy with me asking lots of questions but they are just doing their job so answer them and carry on.
Go have fun!!!
Laura