Babymoon has several meanings. The original meaning is a period of time that parents spend bonding with a recently born baby.
More recently the term has come to be used to describe a vacation taken by a couple that is expecting a baby in order to allow the couple to enjoy a final trip together before the many sleepless nights that usually accompany a newborn baby. Babymoons usually take place at a resort that offers appropriate services like prenatal massage.
Babymoon can also be used for a trip taken by a couple even before they get pregnant. As long as the trip is intended to be a final romantic fling before venturing into parenthood, the term babymoon applies.
The term babymoon comes from the more traditional term honeymoon, which is a vacation taken by a newlywed couple after their wedding ceremony.
|Look up babymoon in Wiktionary, the free dictionary.|
In 1996, the term babymoon was coined in a book "The Year After Childbirth" by childbirth educator and author Sheila Kitzinger.
"The transition to fatherhood is easier when a man can take time off to be with his partner and baby in what I call a 'Babymoon'." 
The etymology of the word babymoon indicates a private time at home for the parents and their newborn to enjoy their time together. More recently, the travel industry has succeeded in redefining the term to also mean a trip before the birth of a child.
In 2004, Lisa Lewis attempted to redefine the term in the Athens Banner-Herald:
"I have learned a brand new word — 'babymoon' ...This is just like taking a honeymoon except you’re pregnant... the purpose is to have one last 'hurrah' as a couple... before baby arrives."
In a July 2007 Reuters article it's also suggested to have a babymoon to "indulge while you can" before the baby is born.
- Kitzinger, Sheila (1996). The Year After Childbirth. Fireside. SBN 978-0684825205., p.203
- Lisa Lewis (2004-12-26). "You may be entitled to a babymoon". Athens Banner-Herald(newspaper).
- Hilary Howard (2007-05-13). "Babymoon: Getting Away While There Are Just Two of You". New York Times(newspaper).
- Jennifer Wood and Brad Perriello (2008-05-18). "Indulge while you can". Boston globe (news paper).