Must I Move My Sims Out? Please Help-- Successfully RESOLVED

If you replace the lot with the new house while in build mode on the lot everything in your household inventory is safe and will still be there. You can move all of those things into household inventory before replacing the House. I should have been more explicit that this is the thing I forgot to do once (didn't move things to household inventory).

I don't know if the same is true if you do it from the Manage Worlds overview though.

Another way to save things is to move everything you want saved into one room and save the room to your gallery.