*Please see addendum at the bottom
I have found two possible explanations for the circumflex: (1) to indicate a long vowel and (2) to indicate an ablative. Both of these functions would seem to overlap!
Earlier grammarians frequently used the circumflex to indicate a long vowel. A practical grammar of the Latin language; with perpetual exercises in speaking and writing. For the use of schools, colleges, and private learners, by George Adler, published in 1858 and available on Wikisource says (among other things about accentuation):
“Monosyllables have the circumflex, when their vowel is long by nature
https://en.wikisource.org/wiki/A_Practical_Grammar_of_the_Latin_Language/Lesson_1#Of_the_Accent. A facsimile is also available on Internet Archive: https://archive.org/details/practicalgrammar00adle
An even earlier source, and therefore perhaps more pertinent to this 1621 poem, is Lily’s A Short Introduction of Grammar Generally to be Used, originally published in 1513. It spills much ink on the accentuation of Latin including the circumflex.
This book was the most widely used Latin textbook in England for almost 300 years, due in large part, I’m sure, to Henry VIII's edict that it be the only Latin grammar to be used in schools (see: https://en.wikipedia.org/wiki/William_Lily_(grammarian) )
It is also available on Internet Archive: https://archive.org/details/ashortintroduct00lilygoog
I include a picture of the first relevant page (p. 195) (to save you a lot of scrolling through the book!). You will see that rule 1 adumbrates Adler’s rule above about the long-by-nature vowel.
Another possibility is that it marks an ablative. The Wikipedia entry for "New Latin”, under the sub-heading “diacritics” states that
“the circumflex accent … was chiefly found over an a representing an
ablative singular case”
Sadly, this has no supporting citations. However, I did find this facsimile of a 1689 book that uses quâ liberally, including in its title, and apparently always as an ablative, which goes some way to corroborating the Wikipedia claim: https://books.google.com.au/books?id=8BJmAAAAcAAJ&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q=qu%C3%A2&f=false
The closest thing I could find for an abbreviation that meant quae was this:
However, this is a handwritten abbreviation from a much earlier period and is not like your quâ at all really. This was found in an edition of Adriano Cappelli’s Elements of Abbreviation in Medieval Latin Palaeography, found here: https://kuscholarworks.ku.edu/bitstream/handle/1808/1821/47cappelli.pdf?sequence=3
I have found the following attested uses of the circumflex in Renaissance/Neo-Latin:
• To indicate a long vowel. Indeed, it is found “exclusively” over long vowels (Lily; Steenbakker).
• To distinguish between homographs where the long vowel differentiates the word (Steenbakker).
• To indicate the ablative singular (a practice adapted from Quintilian’s observation that the apex marked the long a of the ablative singular (Hale, p. 24)) but can also be found over singular genitives of the fourth declension (Steenbakkers). Also see footnote 1 in Gilbert.
• To indicate contraction (amâsse for amavisse, for example) (Hale; Steenbakker).
• To mark an interjection (Steenbakker).
Allan H. Gilbert, « Mock Accents in Renaissance and Modern Latin », in PMLA, vol. 54, no. 2, 1939, https://www.jstor.org/stable/458579?seq=1#page_scan_tab_contents
John K. Hale, « Observations on Milton’s Accents », in Renaissance and Reformation / Renaissance et Réforme, 1995, vol. 331, no. 3 http://jps.library.utoronto.ca/index.php/renref/article/view/11626
William Lily, A Short Introduction of Grammar Generally to be Used, originally published in 1513, p. 195 https://archive.org/details/ashortintroduct00lilygoog
Piet Steenbakkers, Accent-marks in Neo -Latin, (a word search for “circumflex” will take you right to his paper), conference proceedings from 1991, https://archive.org/stream/hafniactaconvent00inteuoft/hafniactaconvent00inteuoft_djvu.txt