A dress is a one-piece garment containing a skirt. What's the word for a one-piece garment that looks like a dress, except it has shorts instead? Are there any qualifiers depending on the length of the shorts?
It is called a 'Playsuit'. If the length of the shorts increases enough that they become trousers, it would become a 'Jumpsuit'.
The one-piece garment with shorts is sometimes referred to as a "romper", as shown here - from a recent online catalog in the US:
Thanks to @RaceYouAnytime's generosity, here are some additional notes regarding "romper":
The OED describes "romper" as originally referring to a garment worn by children, but it can also refer to adult garments of this sort.
2.a. A one-piece garment covering the trunk and all or part of the legs, worn esp. as a playsuit by a young child; (subsequently also) an all-in-one outer garment for a baby.
2.b. An item of clothing of related design worn by adults: spec. (a) a fashionable, loose-fitting woman's garment combining esp. a short-sleeved or sleeveless top and wide-legged shorts
I've always heard that referred to as a jumper
If the lower part is full length and it is a functional garment (rather than a fashion garment), it could be called a coverall (or coveralls). If the top of it is a bib rather than a sleeved garment, it would be called overalls or (rarely) dungarees.
In Australian English this item of dress is a jumpsuit.
The length of the legs does not change the name of the item. The defining feature is that it is a slim-fitting top and bottom in one piece. Slim-fitting in that it is not a 'onesie'. Top and bottom in that it is not a overall/coverall/dungaree that requires a separate t-shirt underneath.
I believe these items were last fashionable here in the 1970's and have had a recent resurgence in popularity.