Did Dido have a choice? She was shot with Cupid's arrow. Before Aeneas’s arrival, Dido is the competent ruler of Carthage, a city she founded. She is determined not to marry again, and to focus on her political obligations- until Aeneas shows up. Also- she tells someone (her sister- forgive me I don't have the book on me right now) that she is feverisgh- so Cupid's arrow sets her ablaze- and we all know fire can be compared to passion and both are destructive!
Also, after her firm resolution not to marry, and then her public affair with Aeneas, or "obsession", at the expense of her civic responsibilities, she would have lost face and power with her people, certainly respect, as she was sought after- so perhaps suicide was a viable option, all things considered. Spurned lovers are now a viable military threat.
"I am a slave to the wonders of the imagination and the cage of creativity." -E. Maggard