Now that's true love.
Sorry to be that guy, but is it, though? Unless the Little Empress does burn the letter immediately, the Emperor has just handed her a burden of enormous responsibility, which comes on top of already being targeted by the Dowager's assassination plots. I have to agree that she isn't very clever.
Love has never been accused of making people clever, quite the opposite. But regardless, handing her that kind of power over her certainly would count as the absolute highest show of trust one could possibly make. But yes, I would expect the empress to show her reciprocation of that trust by burning it anyway.