We didn't get round to putting the forms in til DS was about 3 weeks old, and it only took a week for the payment of our first Baby Bonus instalment. I'm sure it would have been a lot sooner if we had done our bit quicker. From memory, you can fill in part of the forms in advance, and if you get a chance to read through the firms, you can find out all the bits of info you'll need, and have them ready to go.

Having said that, we were told it could take up to 6 weeks after submission of the forms, so you still need to instigate the savings plan that others have suggested above.