Frequently used with a possessive determiner, the humorous phrase beauty sleep denotes:
– sleep, especially taken before midnight, assumed to be necessary to keep one looking healthy and attractive (sleep taken before midnight is popularly thought to be most restful);
– any extra sleep.

These are the earliest occurrences of the phrase that I have found, in chronological order:

1-: From Herbert Milton (London: Saunders and Otley, 1828), by Charles White:

This was one of those small recherché parties, to which only a few of the most chosen of the elect themselves, undoubted, unequivocal rose croix were admitted; being a choice selection from the Almack’s list, purified and doubly distilled in an alembic still more severe than that of the ladies patronesses themselves. Being, moreover, particularly devoted to ecarté, it was attended principally by married women, who, if they had daughters out, generally took this opportunity of sending them to seek beauty sleep in bed before ten o’clock, or else with their brothers to a play, of course in a private-box.

2-: From an article expressing “a very strong opinion as to the serious mischiefs likely to result from the great length to which Parliament has got into the habit of carrying its discussions”—published in The Morning Chronicle (London, England) of Friday 1^st March 1844:

We do not say that the House should never adjourn a debate; but it never should do so, we think, till two or three o’clock. By this means, instead of having half-a-dozen bad, and two or three good speeches, on each of two evenings, you would get the first half-a-dozen bad, and four or five good speeches on the first evening, and there would be no adjournment till the next, merely for the sake of the remaining bad speeches. Many a debate of three nights would thus, we verily believe, be got into one. The rule of adjourning at midnight is a very good one for ordinary occasions, when the night’s debate is over; but when the work is not done, it is very bad economy to take a breathing time of four-and-twenty hours. Unlike beauty-sleep, one hour after midnight is worth two or three before it in the House of Commons.

3-: From a poem published in The Cumberland Pacquet, and Ware’s Whitehaven Advertiser (Whitehaven, Cumberland, England) of Tuesday 11^th March 1845:

DOMESTIC DIALOGUES.
MOTHER AND DAUGHTER.

I’m weary of the world, Mamma!
I never shall smile more;
[…]
For you know that I’m Thirty-four!
Ten chances to one ’gainst my e’er being wed—
[…]
I think ’twould ease my “burning brow”
Were I to go to bed.

“Ah! do my dear! ’tis just eleven,
“You’ll get some beauty-sleep […]”

It signifies little what hours I may keep—
For as sure as ever I fall asleep
A transparency seems to flit before
My eyes, emblazoned with xxxiv.
Like a wind-shaken arras ’twill flutter and frisk—
A kind of numerical Will-o’-the-wisp;
’Tis a mockery, therefore, most cruel and deep,
(And would make any girl about thirty weep)
To be twitted and plagued with your Beauty-sleep!

4-: From The Struggles and Adventures of Christopher Tadpole at Home and Abroad (London: Richard Bentley, 1848), by the English author Albert Richard Smith (1816-1860):

Without doubt the expenses of this lavish entertainment would have fallen heavily on the slender purses of Miss Twits and Bessy; but the jolly man had told them that he would look after all that part of the entertainment, so they took him at his word and let him. His brother too, the steward, came out uncommonly upon the occasion. He promised them that as soon as the boat came back her last turn from Gravesend, he would send up all the cold joints there were on board, and perhaps something else. And if they wanted any glasses—which it was possible they might, their own stock being confined to two tumblers and a Lowther Arcade egg-cup—he told them he would send up hundreds. So they availed themselves also of his liberality. Bessy and Miss Twits were so busy, having to make their own dresses as well as those of several of their visitors, that they were obliged to get an extra hand. And besides the dresses, they manufactured a whole clothes-basket full of silver-paper water-lilies, to make the room look festive; and the first-floor was good enough to say that they might put all their spare furniture in that apartment, which, as their own space was limited, was very agreeable, and of course led to the first-floor being invited, partly out of gratitude, and partly out of charity, inasmuch as there was a probability of the first-floor’s beauty-sleep being somewhat disturbed.

5-: From The Island of Sardinia, including Pictures of the Manners and Customs of the Sardinians, and Notes on the Antiquities and Modern Objects of Interest in the Island: To which is added some Account of the House of Savoy (London: Richard Bentley, 1849), by John Warre Tyndale:

Full many a time had one to appear delighted with, and reiterate thanks for attentions shewn by the family, which the heart tacitly wished to escape. The supper-table groaning with the weight of viands of every description, was a necessary evidence to prove a welcome; but even a long day’s journey and a tolerable appetite, by no means ensure the requisite capacity and compliment of eating copiously of all of them. Full many a time was I denounced as a bad guest for not eating at one repast what would really have sufficed for two days’ meals; and as a Sarde’s capabilities in that respect are by no means inferior to his sentiments of hospitality, it was not easy to prove that my appreciation of the latter ought not to be tested by my inability to compete with them in the former. Dishes after dishes seemed so many incarnations of the demons of nightmare, dyspepsia, and apoplexy; and the wines to be the liquefied regions from whence they came. The lateness of the supper hour is another objection, and “beauty sleep” before midnight is little known in their computation of time. Frequently between eleven and twelve have I heard the summons to proceed to the table, with a mind and body equally unprepared for an hour’s gastronomical campaign.