I remember a while ago people were talking about being able to transplant organisms and such along with scanning them, so you can have your own collection of cool plants and animals, but I haven't heard much about this recently. We know that you can "tame" animals and have them as your pets, but is it possible to capture some and take them with you? Create a zoo? Even if it just means placing the pets in the world and telling them to stay instead of following you, I think this would be pretty cool. And likewise, can you get seeds for plants, etc. and take them with you and plant them in other places? I feel like whether you can or not, there is a big opportunity for mods (or maybe future updates) to step in and allow you to terraform and create your own biomes, and also to do genetic crossing so you can get desired traits form organisms. Like the metallic tree trunks from some and glowing leaves from another, or something. Or maybe red trunks with shimmering silver leaves...
I may be wrong on this but I think you can carry 3 pets with you at all times and you can beam them down to any planet. I don't think they will start to reproduce and what not. I'm sure there will be a mod that can do that and I look forward to it!