I would suggest you consider slowing down, too. The way I see it, there is so much happening already, you don't need to have even more happening at the same time. It's easier to deal with when it's spread out.
Because it's a new relationship, a lot of things will need to be dealt with, and I feel it will be harder if you have other issues linked to living together that you'll have to deal with at the same time.
I don't think it's impossible for things to work out if you live together right away, but I do believe it makes things harder because you have so much more on your plate at once, and not everyone can deal with that easily, especially with poly when more people are involved.
So, try and pull yourself out of NRE for a second, and look at the situation, and consider slowing down. Ultimately, you know your situation better than everyone, but if you didn't have a doubt that it was the right thing to do, you wouldn't have asked for advice, now, would you?
Me: 31F, straight
Seamus: My husband, 32M, straight
Dragon: My boyfriend, 29M, pansexual, married to Fox
Fox: My boyfriend, 29M, homoflexible, married to Dragon