Your model is not listed with a firmware update.
That does not prevent you from trying a couple of the firmware updates at that download page.
They are all small downloads, and run quickly.
If your MacBook does not need the update, the updater will tell you.
That way, you can check for yourself, you might be wrong about the specific model that you have. The firmware updater will know, and can't cause harm to your Mac if the update is not needed, It will just stop without installing anything.
If you have the MacBook model as you say - then Apple has not released any firmware updates for that model.
And - you have exactly the same MacBook as mine.... except you have 2 GB more. I couldn't see the expense for that 4 GB chip...