Dolphin already has some rather robust benchmarking abilities, though they're not utilized often. Benchmarks have been attempted recently as well using only screenshots (search for Wind Waker Benchmark). Fwiw, the FPS tend to remain stable if you're just standing in one spot, so it makes the guess a bit more educated.
About those benchmarking capabilities, delroth added FPS logging in Dolphin. It records the FPS to a text file, one number for every second. You can simply add all of these numbers in a script then divide by the number of recorded seconds to get an exact average. Of course, this only makes sense if you can tell Dolphin to do the exact same thing everytime you run a game for benchmarking. Dolphin can also record movies (as .dtm files) which are essentially save states with button presses recorded at specific frames. It's similar to how SSBB records its "movies".
About those benchmarking capabilities, delroth added FPS logging in Dolphin. It records the FPS to a text file, one number for every second. You can simply add all of these numbers in a script then divide by the number of recorded seconds to get an exact average. Of course, this only makes sense if you can tell Dolphin to do the exact same thing everytime you run a game for benchmarking. Dolphin can also record movies (as .dtm files) which are essentially save states with button presses recorded at specific frames. It's similar to how SSBB records its "movies".