Where possible, dates are in year/month/date format, followed parenthetically with Gulliver's age that year. As a point of reference, it may be interesting to note that Jonathan Swift was born in 1667 and died in 1745.
Here is my timeline:
1661 — born in Nottinghamshire
1675 (14) — goes to Cambridge
1678 (17) — leaves Cambridge, apprentices with surgeon Bates
1682 (21) — goes to study medicine in Leyden
1685 (24) — sets sail as surgeon on The Swallow
1688 (27) — returns, settles in London, opens medical practice, marries Mary Burton (who is probably no older than 17)
1690 (29) — his practice fails, sets sail to the East and West Indies
1696 (35) — returns to England, tries to renew practice
1699/5/4 (38) — sets sail on The Antelope; by this time has fathered Johnny and Betty
1699/11/5 — The Antelope is shipwrecked; Gulliver arrives in Lilliput
1701/9/24 (40) — sails away from Blefuscu
1702/4/13 (41) — arrives back in England
1702/6/20 — sets sail on The Adventure
1703/3 (42) — leaves the Cape of Good-hope
1703/6/16 — Brobdingnag is spotted
1705 (44) — eagle carries Gulliver from Brobdingnag
1706/6/3 (45) — arrives back in England
1706/8/5 — sets sail on The Hopewell
1707/4/11 (46) — arrives at Fort St. George
1708/2/16 (47) — leaves Laputa for Balnibarbi
1708/4/21 — sails to Luggnagg
1709/5/6 (48) — leaves King of Luggnagg
1709/5/27 — arrives in Japan
1709/6/9 — arrives in Nangasac
1710/4/20 (49) — arrives back in England (Gulliver writes he’s been gone 5 years and 6 months, but this is wrong); soon after arrival conceives third child
1710/9/7 — sets sail as Captain of The Adventurer
1711/5/9 (50) — is abandoned on Houyhnhnms Land
1715/2/15 (54) — leaves Houyhnhnms Land
1715/11/5 — arrives in Lisbon with Captain Pedro de Mendez
1715/11/24 — leaves Lisbon
1715/12/5 — arrives back in England; youngest child is now 5 years old (assuming it was born); Johnny and Betty are between 16-27
1719 (58) — poses for frontispiece engraving
1719 (58) — poses for frontispiece engraving
1720-21 (59-60) — writes Gulliver’s Travels; Betty is now married with children
1723 (62) — moves back to Nottinghamshire
1726/10/28 (65) — publishes Gulliver’s Travels
1727/4/2 (66) — writes letter to cousin Sympson