Me and my fiance moved in together after we had been dating for 2 months (really soon I know). It worked out fine though.
We got enaged when we had been dating for 6 months, I found out 1 month later that I was pregnant.
I feel like moving in together was a huge challenge, I mean you never truly know someone until you live with them. We've had our fights, but we learn from them and we move on.
Finances go like this: He pays everything at the moment. I am a stay at home mom, so I can't pay bills.
Before that: We shared the rent, electricity, water, cable/internet bills. We each payed our own cellphone bill, car insurance, etc.
I think that when they love each other so much, they'll do it. Deciding when the time is right...well...usually you talk about it for a bit before you do it. Yes, they should think about finances cause you do need money to live and for bills and such.
Me and my boyfriend, we want to move in together and he does plan on asking me to marry him, when...I don't know, and we plan on having kids one day, but I don't want to move in or have kids, until the finances work out...that's the most important thing. you got to make sure the money's in order. That's how I see it anyway.