Today Anne and Marijn will be moving house. I have looked if there are any medieval miniatures depicting a similar situation and came up with these two images. Both images use carts to transport military equipment, but I guess the same horse and cart can be used to transport your household stuff and furniture.
This image is from Bodleian MS 264 folio 83 verso, dating from around 1340 by the Flemish illuminator Jehan de Grise.
This is from an early 14th century manuscript. The cart is being loaded with stuff (booty?)