We first met Mistress Quickly back in Henry IV Part 1, where the outrageous hostess of the Boarshead Tavern won us over with her rebellious spirit and her zany behavior.
She's back in Henry V and she's as scandalous as ever, especially because 1) she's associated with prostitution and 2) she tends to say and do things that sound dirty without actually meaning to. Remember when Quickly tells us about how awful Falstaff's death was and then explains that he was as cold as ice as he lay in his bed during his final moments? She explains that she "felt to his knees, and and so upward and upward, and / all was as cold as any stone" (2.3.25-26). (Eww!) Mistress Quickly doesn't mean to make it sound like she felt up a dying man, but that's exactly what it sounds like, especially since she uses the word "stone" (twice!) which is 16th-century slang for testicle.
The thing about Mistress Quickly in this play is that her character's not quite as prominent as it used to be. In fact, Shakespeare kills her off toward the end of the play and doesn't even bother to do it on stage. (What's up with that?) Instead, we hear from Pistol that Quickly has died from some kind of nasty venereal disease (probably syphilis): "News I have that my Doll is dead i' th' spital of a / malady of France" (5.1.85-86). Hmm. Does this have something to do with the fact that Falstaff also died from an STD? You decide.