Yes, there's definitely a moon. Just grabbing my copy of Inheritance (I don't have e-books of the first 3) I can find:
Darkness lay all around them, heavy and oppressive. A thick layer
of clouds obscured the moon and the stars. Without the red werelight
Angela held in the palm of her hand, even Eragon and the elves
would have been unable to see.
Inheritance, Under Hill and Stone
They flew on in silence as the waxing three-quarter moon rose above
the jagged peaks of the Spine. By its light, the land looked as if it
were made out of pewter, and Eragon amused himself by imagining
that it was an immense sculpture the dwarves had carved and stored
within a cave as large as Alagaësia itself.
Inheritance, On the Wings of a Dragon
So they don't just have a moon, it's likely comparable in size to Earth's moon in order to cast a similar level of brightness.
Note that Aiedail isn't the sun, it's "the morning star," probably the equivalent of Venus.
Now, however, the morning star, Aiedail, had risen in the east—
heralding the arrival of dawn’s first light—and the time had come to
ready themselves for battle.