The biological definition of the verb “transpire” means to give off water vapour through a pore or stoma. This usage of the word indicates that the mistress’s “willing soul” is seeping through “every pore,” giving her a flushed appearance as her skin is lit with the “instant fires” of her passion. The speaker seems to be saying that while she is still young and in possession of a willing and passionate soul, they should consummate their love.
Vegetables grow slowly and take time to develop, much like the how speaker’s love for his lady would if only there were more time available to them. As it is, they do not have the time. So, despite the speaker’s desire to dote upon his mistress for thousands of years, he instead urges haste so that villainous time cannot steal away the love they have in the present.
The noun “coyness” refers to the quality of acting shy or modest in an attempt to appear alluring. The speaker’s word choice suggests that he believes the lady is only hiding her interest behind modesty, perhaps to avoid accusations of impropriety, and actually wants to pursue a sexual relationship as much as he does.