etiquette question

I've been invited to a 1 yr old's birthday party by her parents (obviously) who are people I like but don't know very well. It's also a party to celebrate their new AC, and is I think mostly geared towards their adult friends, but it is being called "[Baby's] Party."

Here's the question: do I bring a small present? I've sort of assumed yes, since it's a kid's birthday, even though she's little enough not to really understand all of that yet. But I don't know them well enough to know how they feel about consumerism, or what kind of toys she likes or has, etc. Or enough to spend much money. If she were at little bit older I'd bring one of several kid's books that I often give. Maybe I can go to Borders and see if there are 1-2 yr old appropriate books that aren't expensive. As an English teacher I can always make a joke about spreading literature early or something.

And, then, on the other hand, if you're not supposed to bring a present and I do that looks excessive. But if I email the dad and ask him, then he will undoubtedly say "no, don't worry about it" but then if everyone else brought something, I'll feel awkward. Which, since I don't know these people very well (they are dog park pals) I already expect to feel.

Can you tell that I have social anxiety?