The very first thing I ever sewed was a button-up shirt with darting I made with a pattern I drew myself, and I had no prior experience sewing (except a pillow once in school when I was ten years old). It turned out pretty well, just a little bit too large (easily fixable problem). I just got some information online and had my mom show me how to do the button holes. Sewing isn't rocket science. There's a few tips and tricks that are important to know, but basically if you know simple math and can use a measuring tape, you can make your own patterns. So, yes, if you want to take the time to make this, you can do it yourself (even as a beginner). Plus, it's just a costume, so it's not like it has to be perfect.
In regards to how much fabric you'll need. That depends very largely on the pattern and your size. I'm going to go ahead and take a wild stab in the dark and say that you might need at least three yards of your primary material (the main part of the dress) since I'm going to assume you are of average size and most Queen of Hearts costumes that I have seen are short (so I'm assuming your adapted design is shorter than the original). Again though, this really depend on the pattern you've made.
I think for you, maybe a good way to go about doing this is to find some very cheap material (like muslin) and make a "practice" dress. You can get Muslin for like a dollar a yard in many fabric stores (it's around that price at WalMart). That way you can work out all the kinks before using your real fabric, plus you'll have a better idea about how many yards you will need.
As far as cheap fabric goes, you might luck out and get some Valentines day clearance fabric at JoAnne's or some other store that sells fabric. Look around. As a matter of fact, the best place near my house to buy basic fabric is actually the craft department at WalMart. It's not high quality, but again, for a costume you don't really need high quality. And it's cheap. You might also try thrift stores. Maybe you can find some really large clothes at a thrift store, and cut them and use the fabric for some of the smaller pieces.