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Yes, this was how I solved it initially, because I wasn't able to come up with any of the smart tricks (most people seem to just keep count of how many fish are there at each state). Not very nice or efficient but works. :D
Note also that you can solve this without a complexity dependency on n. Most solutions I have seen, including mine run in time O(tD), where t is the maximum value of a timer, and D the number of generation, requiring O(t) memory. (This is assuming we can do the required arithmetic operations in constant time, and each numbers require a fixed around of memory storage; if the number of fish gets huge, throw in an additional log n in the complexities, where n is the number of fish on the final day).