No, she did "Gypsy" after "Happy Hunting".
You could say that "H.H." is the show that kept Stephen Sondheim from writing words and music for "Gypsy".
After her experience with Dubey and Karr (After making some comment on how she should sing one of their songs, she said to the director that they were not to speak to her again. Ever.), Merman did not want to work with another neophyte composer.
So, that's why Jule Styne was added to the "Gypsy" staff.
And after writing "We Take The Town", a musical about Pancho Villa that closed out of town, even with Robert Preston in it, they disappeared off the face of the earth.
(I only know of two songs from it that ever got recorded. Barbra Streisand sang "How Does the Wine Taste" and the songs "Silverware" was recorded on one of their albums of songs from shows that closed out of town.)
"A coherent existance after so many years of muddle" - Desiree' Armfelt, A Little Night Music
"Life keeps happening everyday, Say Yes" - 70, Girls, 70
"Life is what you do while you're waiting to die" - Zorba