I did little to make my daughter interested in astronomy, as it was always around her from the beginning, and she was interested in astronomy from the earliest moment of her life. First of course she was interested in the "huge" telescope that was always there next to her in the dining room - she was quite worried when the scope moved into its new home into my dome. Telescope and dome were actually among of her first words. I had lots of astronomy related books in her reach, so when she was just one, she opened them regularily instead of her fairlytale books, and watched the images inside (surprisingly, her favorite was a huge book, called "High Energy Astrophysics"). She liked to watch whirling galaxies, stars and the Moon. I tried to put kids' astronomy books to the front of the pile, but she always skipped those. At about 1.5y of age, she easily shown the Moon and stars on the sky. As at 2 she could easily count to 10, she even counted the stars apparent to her. At this age she have seen the Moon already through a little monocular.
Now, she's near 2.5y, and just recently seen the Moon and the Jupiter through my larger scope (12" Newt), and enjoyed the view a lot. She also tried to control the scope, but has some difficulties with that. She still has to learn how to view with one eye closed, and I'm not allowed to turn the lights off in the dome because she's a bit afraid of the darkness inside, but she seems very interested in astronomy. But I'm not pushing her into it, so as long as she wants to observe, I support her, but if she decides to become a princess, I'll help her in that too.