I do sign interpertation for American Sign Language, and worked for the Deaf Society of Scotand (British Sign Language) and this is a topic which comes up a lot.
There are so many GREAT reasons to do this. Sign, either "home sign" or recongnized languages such as ASL and BSL, is a great way to teach children to communicate. It will give a child another recourse to language skills, and often is a great way to bond. It will also help the child to be understood when speaking to someone who can not understand the "baby talk" as so much of the home sign (which is what baby sign is classifyed as) is acted out (so to say they are hungry, they may pretend to feed themselves with an imagianry fork).
There are some groups who feel that if you are going to teach a child sign, you should teach them a functional "real world" languages (again, ASL and BSL) so that they have a second language and can communicate with others who speak the language.
There have been studies done to show that children who learn sign or any other form of communications EARLY tend to do better in school overall.
Either way, I think it is a GREAT idea. Go to a class or two and see how it is ...