A playsuit is an item of lingerie consisting of an all in one design where the top half, similar to a negligee, is joined to the bottom half, similar to a panty or shorts.
In terms of underwear in the 1940s, panty girdles were the norm, though panty girdles were generally constricting and not conducive for playing sports.
First up, undergarments - Because she doesn't need to be particularly active in this ensemble, we can assume that Dottie is wearing a standard brassiere and panty girdle.
Ooh, then I guess the panty raid last night was totally uncalled for. Ok, I am going to take a shower and today I will be singing Jim Croce's Leroy Brown.