Is age 19 old enough to travel outside the United States by yourself?

Depends on where they are going. Any world class country it should be fine: Japan, Australia/New Zealand, and Western/Central Europe. Eastern Europe, Latin and South America, Africa, and most of Asia no way.

That depends largely on how mature and responsible the 19 year-old is, and where she will be traveling to.

yeah depends on where you go

should be fine since it's over 18