Finding a whole sand dollar is pretty rare. As a native Californian spending most of my summers on a beach somewhere, I could probably count on one hand how many I've found whole.
When I was a kid, we went to the beach every weekend and my parents followed a tide chart. We would go to the most unpopulated beaches and comb just after high tide. Sometimes that meant getting up at 6:00 am. But that was when we had the most luck finding whole shells. You could find a local bait shop in Carlsbad and ask where you can find a tide chart and if they can recommend any beaches where the sand dollars come to rest. As a kid, it was the most fun looking for those shells that were rare - like a treasure hunt. Even though we hardly ever found them. I've brought that treasure hunting with me into my adulthood. Whenever I'm beachcombing, I'm always looking for that elusive sand dollar and navy blue sea glass.
Good luck in your hunting, and have fun!
Tracy