Noob question about getting a bigger house....

Can i transfer my furniture to a new house?

Not directly. But you can take (most) furniture back into your inventory from the old house and go place it in the new house :)
Exceptions are the furniture pieces that say in the description that they will get destroyed upon removal - like food, the armoire, several Primal furniture and the like.

Thanks! Looks like I'll just lose my stable and mail box. Oh well lol.