"Depends on how much terraforming we want to do. If we just need an uninhabited rock with an atmosphere and no anomalous ambient effects, a couple days, tops. If we want one with a pleasant climate and a nice continent/ocean ratio and edible plants and it has to be pretty, potentially much longer. There might be something appropriate I've already surveyed, if you want me to look through my history?"
So she rummages through her history and finds some options! This one is a moon around a gas giant. The gas giant's pretty nice to look at. The moon would be comfortable unterraformed but doesn't have edible plant life outside the oceans, which at least means imports wouldn't have a lot of competition. It's not convenient to Davlia, it'd be several days at high warp, and it's not near anything else either. This one is full of organic life, which has a certain aesthetic to it but does present a potential hazard. It's got rings and it's near Davlia but also a little close to the Romulans, by and large not super friendly. This one is downright Earthlike except for very low gravity; maybe they could fix that with magic so their bones don't dissolve. It's been flagged for possible Federation colonization, but they haven't established a base camp yet so they could take it and be only provocative, not warlike.
So, gas giant moon? Or they could find someplace astrographically isolated and prowl around there in case they find something they like better.
"We should figure out what we're telling Davlia before we vanish."
"That we're grateful for their aid and a place to live, that we are establishing a new neighbor of theirs as a first step in the creation of an alternative to the Federation, and that we'll visit regularly and more regularly once the evacuation of the people in current danger is complete?" Rúmil offers.
"Not bad. How many people are we talking about evacuating, here?"
"Billions but not everybody is likely to want to go, especially not if they'd have to join the sort of place we'd design and make according cultural compromises. For instance, I assume killing and eating people will be illegal. I'm nervous about establishing communication - I'm not sure it'd be dangerous for them to receive it and it seems firmly established that my universe can't or doesn't reach outside itself and 'nearby' planes. We might have to be vague about the advantages of the Elendil. But figuring out a way to ask is better than just kidnapping people en masse."
"Killing and eating people will definitely be illegal," Fëanáro says firmly. "We can just tell them that there's always enough food and that it's safe for everyone and that you don't have to work and can work on anything you want and nothing will hurt you, we don't have to explain starships or genetic engineering."
"If killing and eating people is illegal we can rule out large proportions of several species," Bella says. "Similar results for other commonsense laws. But we'll get some response and it may be large. We have to invent interplanar earwires first though."
"I hope that helps. - Maybe we should invent a version that does multiperson conversations."
"Who should be called first and by whom?" Bella asks, once that's done.
"But we don't have multi-person conversations, so which one, and who's calling."