Is it a Catholic Baptism? If so, I wouldn't worry about taking anything, unless you want to buy a gift of some sort. Most people would do this for a christening, & being a 1st birthday as well I'm assuming you probably will have something anyway. There are some pretty Christening trinket boxes & things out there that you can have engraved if you would like too
There shouldn't be any rituals that would include you, unless you are a God parent.
& dress would be basically your Sunday best Smart casual I guess. The same as you would wear to a casual wedding ceremony
That is for Catholic baptism though, not sure about other religions
HTH