Advice wanted: First DSLR + lens combo

Getting only a 35mm f/1.8 prime lens will limit your photography to normal perspective. This focal length is good enough for baby whole body shots, but will not be good for closeup portrait. You will also need a wide angle for landscape, travel, and family group photos. A mid range tele will be good for portrait and sports action as your child grows older. Having HD video capability available is handy for family use. I often use the HD video on my Canon 5D Mark II which has excellent quality, and the T1i is probably quite similar. Your budget will not be enough for a fast zoom lens.

Things you will want to have for a nice basic setup and great family photos:
D-SLR with a general purpose kit zoom lens (usually 18-55mm)
A mid range tele lens preferrably with IS (usually falls within the range of 55-300mm)
A fast prime lens like 35mm f/1.8, or 50mm f/1.4, or 50mm f/1.8 for night photos or low light shots where you cannot use flash
An external bouncer flash with diffuser (make sure it can tilt and swivel)
A polarizer filter
A tripod
A remote trigger
A lens cleaning kit
A bag that is big enough to hold all these gears
An editing software like Photoshop.
An external hard drive to back up all your photos and videos

Your budget should include the above essential accessories and peripherals because these things can improve your shots more than a more expensive camera body.

The HD video capability in the newer D-SLRs is a very handy function, with great quality, but it is not a camcorder. You need to either autofocus before switching to video mode, or do manual focus (it has autofocus but it is very slow in the video mode). This video capability is good enough for family clips and baby clips. Audio is decent as long as you don't use any autofocus function or snap a shot during video clipping. For a lot of family clips, I have used the D-SLR video and left my camcorder at home. But for sports action or birthday party video where kids are running around, you will definitely need the camcorder. I found the Litepanel micro to be a very good external LED light for video use.

If you don't need video, the Canon 50D has faster fps and is better for sports action. But your baby will not have any fast action until a few years from now, so not something that important for you at this time.

If you are serious about transitioning to D-SLR, then you should get used to changing lens. Changing lenses is not as bad as you think. Most of the time you know ahead when you need a different lens. If you don't have enough time to switch lens, then use the general purpose lens and crop in to get a tighter shot later in post-processing.

If you really don't want to change lenses or often shoot in dusty or gusty environment, then the 18-200mm lens usually can cover most of your shots. There is compromise, it has more distortions and is a slow zoom lens that costs more than the combined general purpose and tele lenses.

I will suggest you get the separate general purpose and tele lens, and use the left over money to buy a cheap fast prime lens and an external flash. You will get much better photos than using a superzoom lens.

Thanks for the great suggestions!