Hey there!
Now I can't give you much photography advice such as settings and things of that nature. But I can tell you I am a father of four, so I do have some experience with birthday parties and memories I like to keep / wish I had. Given the year of the child being a 1st. birthday party this is about the parents. The child won't remember this party at all. Most parents are so busy trying to entertain their guests to make sure everyone's taken care of they often forget to take photos, or if they do, they're not in them!
So, this is your opportunity. You're going to want to capture the parents with the baby the most. just any moment at all the smiles on the parents faces with their baby. You'll want to get photos of family as well especially the older family because as we all know this life isn't promised tomorrow so those photos with grandparents and family are precious. Take photos of all the decorations, the moms are very proud of their decorating skills and how it turns out because the dads were usually doing something else like making sure the beer is cold. you'll want photos of both cakes, yes both. There are usually two cakes, one for everyone to eat and then the baby's smash cake! Make sure you're capturing ALL those shots of the baby tearing into that cake and the aftermath!
Finally, I think I would just say try to act like you're not even there. Some people hate posing for photos and some of the best photos taken, are when you had no clue that they were being taken! So just capture all the small moments and things going on. I'm not sure that this was helpful, but I have all small children, two-year-old twins, a four-year-old and a six-year-old. So, I've been to and have thrown some parties!
Good Luck and have fun!
~TheColoradoNumismatist