Yes you can get a simm card as soon as you land in just about any country.
There are thousands of parents around the world, including those from NZ, Australia, South Africa who have adult children doing this.
She will be fine. People meet others in hostels and form a group to do something together, go to a particular place / do an activity / plan a trip.
Not the same but at 16 I took my first flight, I was alone and being met by relatives in Australia.
At the first stop there was a sandstorm so we had to land at a tiny airport for a few hours and we could not get off the plane.
Then at the next stop all I had obviously missed my connecting flight, so QANTAS re routed a plane.
I arrived at my destination about 6 hours late.
This was the early 1980s. I was fine. I had no way to contact my relatives at either end, but I was fine. I had quite a sheltered upbringing and I was still fine.
She will not be alone, she will be among loads of others doing a trip round the world in various stages and directions.
She will be fine.