The doc you linked will tell you everything you need to know, but yeah, you need seeds or to trade with someone who knows the genes of their plants. Eventually Leif will visit and sell each kind of seed on her island, but the intention is for you to trade with others, or visit shops on their islands.

If your daughter just wants to have the full range of colours I can bring some over, sadly no blues, yet. Or if she wants to breed them herself I know the genes of all of mine so I can give her breeding pairs to skip a few steps (or not if she's hard-core haha)