...And this from The Word Guys...
"To trip the light fantastic" appears to come from the powerful poet of loss and regaining. Yes, John Milton's L'Allegro (1632) gives us the first usage.
Haste thee Nymph and bring with thee
Jest and youthful Jollity . . .
Sport that wrinkled Care derides,
And Laughter holding both his sides.
Come, and trip it as ye go
On the light fantastick toe.
The rest of the 17th century didn't exactly tear the phrase out and flop it into common usage. In fact, only in the late 19th century was the phrase pulled free into the mouths and pens of the rest of us. Somerset Maugham used the full expression so very well in Cakes and Ale (1930), "The muse does not only stalk with majestic tread, but on occasion trips on a light fantastic toe."
So, if you keep in mind that Milton uses "trip" in the sense of to tread lightly, to skip, to move nimbly and lightly (still listed as such in the OED), might we even go so far as to say dance, then you see that the phrase really implies moving lightly and well on a toe that is both light and fantastic. It is not a fantastic light, but a toe that is both.