We live in a beach town. DD was around 13 months when we arrived here and in the summer we are at the beach several days a week. I think it depends upon what kind of beach you are going to be visiting. That first summer, all we really needed were a good hat, lots of sunscreen, bathing suit (two piece for easier changing), and a cover up/towel (and sunglasses if she'll wear them.) A simple shovel/bucket set is nice. They are easy enough to pack since you can pack clothes inside the bucket. We have the Green Toys sand play set and it's perfect. At 13 months, I would just take the bucket and shovel. I love water socks at the beach!!! DD doesn't like the feeling of sand between her feet and sandals but she needs something on her feet if the sand is too hot, or it's rocky, or we're walking from the parking lot, so water socks are great for protecting her feet when necessary. Iplay makes some:
I think Speedo does as well... They are a fabulous investment!
iplay also makes reusable swim diapers. I would pack up a small pack of disposables even if you are thinking of going reusable since we once lost a reusable on vacation unable to clean it properly after a major stomach upset...
They don't make them anymore, but once upon a time, Lands End made a one piece infant suit that had snaps like a onesie. It was so wonderful for beach diaper changes. I wonder if you could still find them on eBay?
Anyway, those are just a few things off the top of my head. Hope you have an incredible vacation.