You are, in fact, thinking of Friday, by Robert A. Heinlein. Plot summary, from Wikipedia:
The book's narrator is Friday Jones (often going under cover name Marjorie Baldwin and using both surnames somewhat interchangeably). Friday is genetically engineered human (known as an Artificial Person or AP) in many ways mentally and physically superior to ordinary humans. There is great prejudice against APs so Friday conceals her status.
Employed as a highly self-sufficient “combat courier in a quasi-military organization”, travelling across the globe and to some of the near-Earth space colonies. Friday is returning from her latest mission when she is captured, tortured, raped and interrogated by an enemy group. She is then rescued by her own people, who tell her that her highly critical mission was in fact successful as her captors failed to find the data she was carrying in her body.
After recovering from the ordeal, Friday takes a vacation to visit her group family, composed of several husbands and wives and many children. In an argument over racism, Friday reveals to her family that she is an AP, and they promptly divorce her.
On the way back to her company's headquarters, she meets and befriends the wealthy Tormey family. Friday is their house-guest when a worldwide civil emergency known as Red Thursday occurs. Various groups claim credit for the assassinations and sabotage, but Friday later learns that it is the result of a struggle between rival factions within the ultra-powerful Shipstone corporation. Her last mission was to carry information about the attacks before they occurred.
Facing detention under martial law, Friday kills a policeman who attempts to arrest her and Georges (a member of the Tormey family) as non-citizens. The two become fugitives, traveling across the various countries of a Balkanized North America as she attempts to return to her headquarters. After several adventures, she succeeds in rejoining her company, leaving Georges to rejoin his family. However, Friday's boss soon dies and the organization disbands, rendering her temporarily homeless and unemployed. She learns that her boss left her money in trust, to be used only for the purpose of relocating to an off-Earth colony of her choosing.
Friday eventually finds another courier job which will incidentally allow her to visit and evaluate several of the colonies she wishes to explore. However, after embarking on an interplanetary cruise ship for her mission, she learns that agents of her employers are watching her constantly, and that she is a virtual prisoner on the ship. Realizing the top-secret nature of her mission, she fears that her employers will kill her when it is over. While the ship is docked at a rustic colony world, she escapes with the Tormeys, who have been on the run since the policeman's death and happen to be fleeing Earth on the same ship. After evading the ship's authorities, they all join the colony and settle down to lead a quiet life.
Not mentioned in the plot summary above is that the mission mentioned in the last paragraph was to bring an embryo to the rulers of one of the other worlds, and that's what you're thinking of - it wasn't using her 'pouch', as she had been told; it was implanted in her uterus - which is, after all, ultimately the best way to transport an embryo.
Friday at ISFDB