Hi Anastasia!
Disney does a great job at trying to accommodate families with children of all ages! Even the smallest of miracles, like your young one :-)
I also had slight reservations bringing my 18-month old a few years back, but soon found there is still plenty for them to do at the theme parks!
Here is a great link that Disney provides, detailing those experiences bringing a pre-schooler to Disney World: Bringing Preschoolers .
My son had loads of fun at Animal Kingdom, and yes, any age can get on the Kilimanjaro Safari journey. The vehicle, which I call a jeepney, is safe, and even though you're going through areas with water and mud, the vehicles barely jerk around at all (apparently have great suspension :-).
In addition to the Kilimanjaro Safari at Animal Kingdom, your child should really enjoy the Discovery Island Trails, Boneyard, and Triceratops Spin.
Hope you and yours have a magical time on your visit!