RoyalGuard said:
Not coming from a bilingual family, I don't know about the kinds of problems/opportunities that there are in learning multiple languages.
There are definite advantages. The brain centers responsible for the languages learnt during childhood are far more efficient than those responsible for languages learnt later on. Besides, being fluent in more than one language helps making connections and learning a third or a fourth during adulthood.
But in order for this to be efficient, you should master the language you teach your child. That means, start learning now! It's also useful to use one language per parent/adult with frequent contact. Rather than having her read lips one day and communicate with signs the other, you could chose one way of communication, and your partner, the other. In case you're a single parent, I guess you should choose sign language, and have other person or persons speaking clearly to her.
Please note, speaking clearly is not the same as speaking slowly, or overstressing syllables, because it alters the results. Consider the way you pronounce the T in "too" and in "Anita", and look at yourself in the mirror while you do it. You'll see there's a difference, and pronouncing "A Ni Ta" is not the same.
As for the drawbacks, bilingual children tend to confuse both languages during early childhood. They're unsure about which one to use with each person (that's why it is helpful to share the tasks). At first, it seems like their language development is slower than other children's (especially being deaf), but then, around 3 or 4, they suddenly start differenciating. In the meantime, the person who talks to her orally should be able to understand sing language, but try to avoid using it, even if the child seems to understand them better this way.
On the other hand, the difficulties of learning a second language aren't as tough as somebody pointed out (sorry, I can't locate the message right now, but it said something like "have you ever tried to read the manual of a foreign device?"). God knows why they don't hire professional translators, but being proficient in a foreign language is kinda possible. English isn't my first language, it isn't even my second. And I learnt it as an adult. I'm aware that what I write will never sound idiomatic, but I guess it's easier to understand than most of these manuals.