As an expectant father and assistant photographer I'm sure our daughter will become very used to having a lens put in front of her. In the past when asked by family or friends to take photographs of their little bundles of joy, the one constant dilemma is how to attract and maintain the attention of a little one. Ways to overcome a sporadic attention span can vary from child to child; attaching their favorite toy to the top of the lens or dangled (out of shot) above the lens is a key trick. This is, of course, no substitute for having the camera ready for those little moments when your child is lost in thought, debating in their little head the best way out of recession for Europe or whatever it is they’re thinking about…!
Don't be afraid to shoot loads and be experimental. It's free and you can always delete the bad ones. I would also advise on editing 90% of what you take. I’m sure that will be some task, but believe me, you don't want to bore people looking at what is effectively the same shot 20 times over. Pick one photograph from each situation and only show that one (nobody needs to know it took you 50 shots to capture that one image).
If you have a camera that’s fully manual you might like to try a very shallow depth of field, with the point of focus being an eye, hand or foot, or indeed whatever will draw the viewer’s attention to the heart of the frame, while allowing a nice soft feel to the image. If you decide to use this technique, be prepared to shoot loads and edit heavily, as babes tend to move a lot! You may find the point you had originally thought of, or planned to have in focus ends up being soft with an elbow or leg in focus instead, not necessarily what you wanted! F1.8 to F2 should be good for this depending how close you get and the lens / camera.
Finally, as with all photography look for good light situations - light can make or break an otherwise amazing picture. Start looking for an area of the home where the sunlight looks beautiful and then use that as your "studio", moving around the light source creating ether a back light effect or side light. If not too strong, a direct light can really bring your subject’s eyes alive. (NB - never ask baby to look directly into the sun! Obvious point, but you just never know!) You can also use a piece of white card (or silver foil) to reflect light into any situation.
Most of all my advice to you would be to relax, have fun and enjoy capturing one of the most exciting times in both your lives.