Sun and moon: male or female?

As already pointed out by Peter Shor, The Walrus and the Carpenter, which might exemplify children's literature (including, of course, the child inside everyone of us), has genders for the sun and the moon as quoted by yourself.

Etymonline, if you count it as trustworthy, confirms the Germanic genders for the sun (feminine) and the moon (masculine) in Old English.

The flip of genders for these two (or rather, the loss of genders and the establishing of a so-called poetical gender) came later, as claimed here. Quote:

The modern English poetic usage when personifying the sun and moon has taken up the French or Romance gender for sol (masculine) and luna (feminine), instead of retaining the Germanic grammatical genders where the sun is feminine and the moon masculine.

(Ragnhild Ljosland, Masculine and Feminine in Dialect)

I believe the sun is usually male and the moon usually female. For example, from Lewis Carroll's The Walrus and the Carpenter,

The sun was shining on the sea,
Shining with all his might:
He did his very best to make
The billows smooth and bright–
And this was odd, because it was
The middle of the night.

The moon was shining sulkily,
Because she thought the sun
Had got no business to be there
After the day was done–
“It’s very rude of him," she said,
“To come and spoil the fun!”

If the genders were reversed, I am sure that it would be much less disconcerting to English speakers than if they were reversed in German or French, where they actually have grammatical gender. When this poem is translated into German – Das Walroß und der Zimmermann – the moon and sun switch genders; whereas I would be surprised if their genders were switched in anything translated from German to English.

And in fact, it seems that Tolkien, in The Lord of the Rings, makes the moon male and the sun female. See this question. And most readers aren't greatly disconcerted by this shift. One wonders what genders are assigned in the French translation le Seigneur des anneaux.

Both pairings are adequate, since Sun-female/Moon-male is the original Germanic reading and Sun-male/Moon-female is the Latin(ate) version. Provided that you have some knowledge of why you are picking the one or the other, both are usually fair; the only exceptions would be when you have a strong thematic connection to Ancient Germanic/otherwise Germanic/Anglo-saxon/Old and Middle English up to the Renaissance, where you'd have to go with the first (eg. if you're translating from the Exeter Book you will have to write about the moon and his beams), or when you have to do with the classical Greek or Latin tradition, when translating from a Romance context, or when referencing a Neolatin-originated tradition (eg. if you write a follow-up to Ariosto's "Orlando Furioso", Astolfo will fly to the moon because she keeps lost objects).