Surround her with other people who love her. Those can be family members or dear friends. The whole "it takes a village" thing can make a child feel more secure. At some point, it may make sense to discuss that plans are made to care for her if something happens to you - but think about when/whether that would be right.
Show her active and involved 80 and 90 years olds - Betty White, Gloria Steinem, Ruth Bader Ginsburg and so on. Go across the spectrum of politics, activism, celebrities, neighbors, etc. Be sure she has images of the Gloria Steinem "80" vs. the nursing home "80"! Let her know you plan to be an active grandparent for her children and helping her through the tough times when her children first confront mortality at age 10. Also point out that we know a lot more about nutrition, the science of aging, epigenetics (repairing damage to cell function and gene expression), and other things to fight off the challenges of aging.
When I was a kid, I felt my parents were ancient because they were 32 and 33 when I was born. That's until I had my child at 37. And my girlfriend was 47 when she found her exhaustion to be diagnosed by her doctor as early pregnancy! I also remember being so horrified by the idea of life insurance.
I think it's a phase and she'll get through it, but that doesn't mean to ignore it. Let her know every child feels this way at some point, and that the choices people make in their teens and 20s and 30s might make some of her friends' parents even less likely to have a long life span than you. The advantage is, she can see that you have survived (or avoided) the risky teen behaviors, the "invincible 20s" temptations, and many other killers of younger people. Your smarts will guide you through your 50s and 60s and 70s just as they guided you in earlier decades. Let her know you expect the same of her.