Mandrakes (Hebrew duda’im) were a Middle Eastern plant used as an aphrodisiac (see Genesis 30:14–16). The roots look like a human torso. The word is a play on "my lover" (Hebrew dodi).
at our door: All sexual pleasures are now available to them, and she will share the delights she has saved just for him.
new...old: She thinks about the sexual experiences they have already had and new ones they will try.