J.R.
I have two tips for you:
First, even though it seems counterintuitive, when she bites DON'T try to pull her off the nipple instantly -- you're much more likely to get scraped and her instinct may be to clamp down harder to keep a grip. Instead, smoosh your breast firmly towards her face, then immediately use my second tip:
Pinch her nose. She will open her mouth to breathe. This will not come naturally to you at all when you're in pain, at least not at first!
Then give her a firm NO BITING, if she's awake, or reposition her if she's sleepy-nursing and not ready to stop (which is when my toddler tends to bite).
The laughing thing is simply a response to your sudden and unexpected attention. Soon enough, she'll break out in tears instead...which is a sign she's getting it...and then the biting will stop, except, in my experience, when she's very tired and not paying attention.
Hope these tips give you the break you need so that you can wean when you feel she's ready. We're still going at two.