The Argive queen is Helen, also known as Helen of Troy. The hint that Argos could refer to Mycenae (Helen was the wife of Menelaos), combined with the mention of beauty (see Marlowe's "Was this the face that launched a thousand ships / And burnt the topless towers of Ilium?" in Doctor Faustus) was very helpful.
The phrase "Argive queen" was used in George Chapman's translation of Homer (the famous Chapman's Homer that impressed John Keats). Chapman´s translation of Homer´s Iliad, edited by Richard Hooper, 2nd edition, 1865, contains the following lines:
Amongst her maids was set the Argive Queen,
Commanding them in choicest works.
Hooper provides the following gloss:
Argive queen - Helen, formerly queen
Other sources, somewhat ironically, identify her as "Helen of Troy", even though Troy was famously never her real home, let alone that she was a queen there. See for example:
- A Ben Jonson Companion by Dewey Heyward Brock (Indiana University Press, 1983): "Argive Queen: Helen of Troy";
- The Ben Jonson Encyclopedia by D. Heyward Brock and Maria Palacas (Rowman and Littlefield, 2016): "Argive Queen: Helen of Troy. Mentioned in Forest 12". (The Forest contains the "Epistle to Elizabeth Countess of Rutland" quoted in the question.)