Since she offered to help you at the birth and you are such close friends I would assume that she is not charging you but for peace of mind I think you should double check. If you don't feel comfortable outright asking her if she's doing it for free or charging, maybe you could make a casual remark or joke about getting a discount for her services and see how she responds.
My friend, though not an official doula, attended my son's birth and I gave her a magazine subscription, a bottle of wine and a gift certificate for a massage as a thank you. I then qualified as a doula and attended her son's birth a couple months ago. I didn't charge her a penny but she got me a lovely hardback journal, a pair of argyle slipper-socks and 50 in cash. I think with friends a nice gift is the way to go.