Ahmed Hosny was correct in his answer. It required the many parameter to be set to True to work.
So final version of the CartSerializer looked like this:
class CartSerializer(serializers.ModelSerializer):
cartitem_set = CartItemSerializer(read_only=True, many=True) # many=True is required
class Meta:
model = Cart
depth = 1
fields = (
'id',
'date_created',
'voucher',
'carrier',
'currency',
'cartitem_set',
)