I'm a birth photographer and I think the world needs more of us :) In answer to some of your questions:
I absolutely agree you should not charge. Before you step foot in a birth you should be comfortable controlling your camera in manual in your own house at night without a flash. This is the best way to practice for a birth environment. It is NOTHING like shooting outdoor portraits of your kids or controlled shots with an external light source/flash. Your camera is good but not ideal for a birth setting because the D300 still has pretty bad noise handling in low light so you'll also want to practice editing noisy/grainy images so you can find the best combo of ISO/Aperture/Shutter to reduce noise as much as possible for your body and lens. And if you don't have a prime lens with an aperture of at least 1.8, get one. You can pick up the 50mm 1.8 really inexpensively. You'll probably also want to process in black and white and that's an art in and of itself. That, too, is something you can practice now with ordinary photos of your kids.
When you start charging for births, the best advice I ever got was to decide up front what my ideal pricing structure would be and then offer a temporary reduction on that. So after I had some free births under my belt (and you should not need 10 - a few in different environments should be plenty for you to decide if you can make this a profession), I did a few for 50% off full price. It is MUCH easier to get rid of a discount than to raise your prices!
You will want to work up a model release and insist that all your portfolio-building clients sign. If you do not have work to show, you will never get hired. And then be VERY careful about the images you use. Not only do you NEVER want to take advantage of a client's trust but you also don't want to portray yourself to perspective clients as a photographer who will post graphic images. Insist on the model release - it is your marketing! Also never release full copyright on any images. Always provide a print release (if you are selling or including digital images) that explicitly says you retain copyright. This is industry standard.
When choosing how to price yourself, try to do a cost analysis. If you are at a typical birth for 8 hours and you take 4 hours to edit the birth plus 2 hours for a pre-birth consult, meals and parking at the birth, the cost of supplies for the CD/DVD, wear and tear on your equipment, time to deliver or cost of mailing the CD, etc you won't even make minimum wage at $200 a birth. I understand you, like all of us who work in the birth world, aren't in it for the money. But there is a difference between not being motivated by money and devaluing yourself! And never mind how you feel about yourself, you will be treated only as well as you treat yourself. Your most difficult clients will likely be your portfolio-building clients and your most grateful will be the clients who pay full price. This isn't always the case, obviously, but it's a rule of thumb in all areas of life. Do you want clients who really value you at their birth and value photography? Or do you want clients who treat you badly or place no real value in what you do? And of course you WILL burn out if you don't make enough to at least upgrade your equipment, pay your sales tax (every birth session has to be taxed!), pay your income taxes, pay your liability insurance and still feel like you aren't being robbed, right? You won't EVER get rich shooting births (just like midwives aren't getting rich and doulas aren't rich). But you have to make enough to at least break even!
Finally be sure you can handle being on call. It's hard. You have probably thought this through since you considered being a doula. It's the same on-call commitment. No vacations, no day trips. My brother just got engaged and I'm booked through November so if he picks a wedding date before December of this year I won't be able to go to his out of state wedding. Missing your kids birthdays, Christmas, etc. And if your client goes into labor at night (likely), you'll have to function on no sleep unless you have daytime help to relieve you. If your client goes into labor during the day you lose an entire day's productivity and have to play catch-up. It's hard no matter what. The burnout and turnover rate for birth photographers is HUGE. Most of us limit the number of births we take per month to ensure availability but also to ensure that we don't burnout and that we can have some semblance of a life. But it is also super-hard to say no. So keep that in mind. If you don't want to burn out, take it easy from the get-go.
Ok so that's way more than you asked for, really. I'm happy to talk about things privately if you like. I hope I don't sound too negative. I think it's best to go into anything new with as much info as possible and you already know all the positive things :) It really is the best job ever and like I said, we need more birth photographers out there! Good luck!