I have four (soon to be five) children, and although we actually have a girls' and boys' room, all four kids currently at least start the night together on a king-sized mattress in the girls' room.
We never pushed this, this is coming from them; in fact, they complain bitterly when they have to be separated from one another (due to illness, etc.)!
Will this change as they age? Likely yes, but I really don't believe it's the sq. footage of your home that kids remember, anyway. It's certainly not what sticks with me from my own childhood (I was the oldest of five.) I grew up in an average neighborhood in an average-sized home, and while I was peripherally aware there were families who had both more and less than I did, it never made me feel either enriched nor deprived in any way. My home was just that, my HOME; it was my safe haven, my refuge, and how big or small it was or the relative size of my bedroom never entered into the equation for me.
As for what I've done since having my own family, our first house was 1400 sq. ft.; we had 3 kids there and still felt like we had plenty of room to spare. Then we moved to a new city into an 800 sq. ft. apartment for 6 mos. until we could afford to buy another home. Our current home is around 2000 sq. ft. and could easily see us through several more children, if we chose to have more (I think we're done with 5, though...)
Interestingly, for almost a full year AFTER we had moved out the small apartment into this house, my oldest child repeatedly told me he wished we still lived in the apartment complex.
"Why?" I asked him, baffled, since I was very much enjoying our new, larger space.
"It was so cozy there, mama," he said. "Everything and everyone was right there all the time. I liked that better!"
Out of the mouths of babes (okay, well, 5 yr. olds, lol)! DH and I really appreciate the open floor plan of our current home and having some space to ourselves, but our kids (at least at their current ages) really could care less about "personal space." They care far more about "being comfy and cozy with everyone and everything right there."
When they do start wanting more privacy (as teens), we'll do our best to give them a space for that, or, should that prove impossible, find ways for them to enjoy privacy outside our home.
*edited to add... Mel, I meant to throw this out as a suggestion -- is there any way in your new house to consolidate EVERYONE'S clothes and store them in one place? Like have ALL the dressers in one area, and everyone just goes there to get dressed in the mornings? We've done that for all our kids (there's not enough room for our clothes, too, unfortunately) and it's actually worked really well, not to mention that the dirty laundry tends to end up all in the same general area, too, instead of on the floor in several rooms. All the laundry hampers are in that area, too. And it makes putting away clean clothes a lot easier, as well. Just a thought!