Roy,
Welcome to the neighborhood. First off, I'd say that the general tone of your original post could be taken in a number of ways. And I can see both sides. I know what it feels like to have a certain skill set and have people I have worked for dump me and do it themselves (rewriting your own will after you've paid an attorney to do it, or using a Will-In-A-Box software kits from Staples or Office Max is a mistake...I'll stop lest I'll mount the soapbox). The other side of this whole thing is that you want to be able to capture your daughter as she grows up, and you're asking for help on how to do it. I'll explain how I got into this, and what I did.
I shot both Canon and Nikon film cameras in high school, and didn't really have a preference. After I graduated and lost access to those cameras, I kept asking my parents for a camera for birthday, Christmas, or for any other reason. They always said no. I decided to ask a local photographer what he used, and what he would suggest. He is a Nikon shooter and said that if I purchased a Nikon he'd be able to help, and not having a preference, that's the direction I went when I made my purchase. I looked at a variety of different cameras, played with them, fiddled with them, and eventually decided on the D5000. It's everything I needed as my first DSLR.
My suggestion to you is to find someone local who sells cameras, or find a chain camera shop (please no one throw fruit at me for that) and see what they feel like in your hand, what they do for you when you look through the viewfinder, and how you feel about the size, weight, and cost you're going to put into this. Alternatively, if you decide to go the route of a point and shoot, there are some seriously good offerings out from Panasonic, and Canon. Like I said before, I shoot Nikons, but my parents have a Panasonic and a Canon and love them both. For me, it's easier having to know only one set of controls.
Buy the camera first, then start thinking about lenses, but don't go bananas right away, lest you have spent a TON of money (this hobby/profession gets expensive in a HURRY) only to have found that you're just not that thrilled with it or don't have the time to dedicate to it. Take an entire weekend and go nuts--shoot everything you can find from your daughter to your wife to the neighborhood kids to the landscape around your neighborhood. Get to know your camera. Get to know what it does in certain situations and what it won't do. Take bad pictures, learn from them, and try again. Keep a notebook of what works and what doesn't.
Regardless if you buy a D3x or a point and shoot, if you can't compose a picture, a $7,000 camera and a $2,000 lens isn't going to make things any better. Lastly, if you buy a DSLR, go to a book seller and purchase the David Busch (like the beer) Guide to that camera. Read it cover to cover with your camera in your lap. Read it before bed. Read it on the john. Learn it--having some really cool features does you no good if you don't know how to use them!
Lastly, now that you may have acquired a DSLR, don't start a fan page for your photography as a number of people I know have done--just as owning a fast car doesn't make you Al Unser, owning a DSLR does not mean you can hold yourself out as a professional photographer. It's obnoxious, ostentatious, tacky, and dishonest. I am far from a professional photographer, but some of the trash these people are trying to pass off as professional level work really irks the hell out of me.
*Soap Box dismount...*
What's the point of all of this--have fun and get good at whatever you decide to do with whichever route you decide to take this. Point and Shoot or DSLR--it doesn't matter to us which you do, but we want you to shoot happily and shoot great photographs of your daughter for you and your wife to enjoy for many, many years to come!