An Early English Books Online search turns up multiple relevant matches for the phrase "loose woman" around the year 1600. (The EEBO database covers the period from 1475 through 1700.) The earliest of these matches is from a 1598 translation by John Keper of Haniball Romei, The Courtiers Academie Comprehending Seuen Seuerall Dayes Discourses:
The Marquesse was satisfied with this answere, and the Count of Scandiano, a most valorous Knight: Mee thinkes sayd he, that you, sir Knight, haue very vniustly placed the adulterer in the number of men dishonored, bicause custome is contrary; seeing that men, are not onely, not ashamed to commit adultery, but as of an enterprise honourable, they haue no sooner performed it, as that therof they vawnt, and make great boast: ney ther is it intended, that any one should euer be refused, in comparison of honour; for being an adulterer, notwithstanding that of these, the number be infinite. I am desirous therefore, that you would giue me to vnderstand, how it may be, that an adulterer should be infamous. A man, answered the Knight, committeth adultery in two sortes, in one, when he being bound, falsifieth the oth of matrimony, frequenting with a loose woman. And in this, although he be worthy of some blame, yet looseth he not his honour, because he iniurieth none but his owne wife: in the other, when married or vnbound, he vseth the company of a woman married. And this man remaineth dishonoured, be∣cause he finneth extreamely against the vertue of Temperance, and faileth in iustice, hee beeing a greeuous iniurier or destroyer of an other mans honour; the which (as I haue saide) of all other goods externall, is the most pretious: and therfore deseruedly by the lawes, is there imposed on adultery a greater penalty, than on theft, because the adulterer endamnifieth in honor, and theft but in goodes.
The instance of "loose woman" in this case is striking because the speaker explicitly associates it with a "bound" (that is, married) man. It is tempting to read "loose" in this case as a morally neutral term meaning simply "not bound by wedlock to a spouse." However, other instances from approximately the same period suggest that the "loose" in "loose woman" was already intended pejoratively.
From a 1599 translation of Luis de Grenada, A Memoriall of a Christian Life Wherin Are Treated Al Such Things, as Appertaine vnto a Christian to Do from the Beginning of His Co[n]uersion, Vntil the End of his Perfection:
THE VI. COMMANDEMENT. Thou shalt not commit Fornication.
Albeit that in all sinnes offence may be committed by Thought, Worde, or Deede, yet in this sinne of the fleshe, it doth more vsually happen than in any other. And in what manner soeuer of these three kindes he shall offend, the quality & circumstance of the person with whom he offended ought to be expressed. (As whether it were with a Virgin, or a single loose Woman: or with another mans Wife: or with his neere Kinse-Woman, &c.) according as we haue before declared.
Here again the "loose" woman is explicitly unmarried, but sexually experienced.
From Thomas Dekker & John Webster, North-ward Hoe (1607):
Mistrisse Maybery. Speake Sir did you euer know me answere your wishes.
Greene-shield. You are honest, very vertuously honest.
Mistrisse Maybery. I wil then no longer be a loose woman, I haue at my husbands pleasure tane vpon me this habit of iealousie: Ime sorry for you, vertue glories not in the spoyle but in the victory.
In this play, Mistrisse Maybery is in fact a chaste and honorable (married) woman. When she says that she will "no longer be a loose woman," she means that she will no longer pretend to be one.
From Gervase Markham, The Dumbe Knight: A Historicall Comedy (1608):
Meshant. Are these the winding turnes of female shames, / Loose womans gamboles, and the tricks of sinne? / And are we borne to beare these suffrages? / O hee thats tide vnto a brothell bed, / Feeles his worst hell on earth, and may presume / There is no sicknes like his pestilence: / Well, what the issue of this iest will proue, / My wit but yet conceiues and after time / Shall perfit it and giue it liberty, / In such sort, that if it true fire strike, / A world of Apes shall study for the like.
In this scene, Meshant has just observed an amorous lord and the unfaithful wife of an orator arranging a tryst for the next day. The "loose woman" whose gambols he has just observed is married but not overly concerned about that fact.
From Anthony Nixon, A Straunge Foot-Post with a Packet Full of Strange Petitions (1613):
My meaning is not to disparage learning, because it is hard to attaine dispraise honour, because it is difficult to get: discourage Prentises, because their beginnings are laborious: for I haue read that the base of Pernassus is full of briers, thornes, and thistles, but the toppe, plaine as heauen, & smooth as the Moones face. I haue heard that the steppes which ascend to honour, are like the staires which mount to the hight of a Maze, many and endles. The dores conducting thervnto, infinite, and intricate, but the top like the toppe of Olimpus, and the roomes pleasant, and spatious, garnished with more then mortal obiects. And I know by Experience that the skill and secrecy of mechanicall Artes, are not got (like a loose woman) at first sight. Neither will yeild any great proffit at first labouring, any more then a barrein ground at the first sowing, I doe not therefore Cauill with my calling, nor am pensiue for the paines I indure; but the originall of all my sorrow is a Mistresse so peeuish, proude, petulant: oh sifas dicere.
The speaker here is an apprentice. The sense of "loose woman" here is pretty clearly "one who can be got at first sight," regardless of her marital status.
By the turn of the seventeenth century, the term "loose woman" had begun to appear in published English writing. Its earliest appearances in EEBO search results—from books published in 1598 and 1599—leave room for interpreting the sense of "loose" as being merely "not bound by marital obligations"—that is, single. Within a decade, however, "loose woman" appears in a play in which the speaker applies the term to a sexually promiscuous woman who is married, so it seems quite likely that "loose woman" carried a sense of immorality in the earlier examples as well.
It certainly appears to be the case that the phrase "loose woman" is considerably older than the phrase "loose morals." The earliest EEBO search match for the latter term is from an anti-Catholic polemic published in 1680.