I don't think you will see any new cameras before the end of April... I expect the 70D at the end of June (in time for holidays) and the 7D2 - if there ever is such a thing - in late October. This means your selection space is limited to what's available now.
@Freelancer - My recommendation on the 7D is that it's a wonderful camera - at the current price you get a great deal for your money. Sure, you could spend a couple of hundred dollars less and get a 550 or 600 but the user interface and versatility of the 7D gets my nod.
@OP My take is that the 7D is such a huge upgrade from a 20D, image quality will not be your limiting factor. Be aware that it's a more complex camera to set up, so you need time to get it right. If this is your route, do not delay.
How about looking to see whether you can get a 7D under the Canon Loyalty Program? If you have a broken (or even not broken) Canon P&S Camera, you can get quite a lot of credit on a refurbed SLR.
On full frame...
The often underappreciated point is that the upgrade to ff can be a lot more than the cost of your camera body and your first lens. The 24-105 L is a great lens but it's a stop slower than the 17-55, so any benefit you had with the noise performance disappears because you use higher ISO. To see a real improvement, you'd be looking at a 24-70/2.8 and that would probably drive your budget a bit far. If you decide to go for a 6D, you will also need to think about a flash.
I don't recommend strobing a baby - just about anything will startle them - but you will probably want to think about a light panel or at least a reflector. Of course, a reflector will work for both crop and ff, so it's something you might consider chasing down anyway.