Well, Talmud doesn’t have any insight over inviting your son’s girlfriend on vacation, but we can glean some insight from rabbinic texts on marriage (gulp!).
We have a tendency to see our ancestors’ relationships through the lens of “Fiddler On The Roof”, with arranged (often unhappy, usually by force) marriages. In fact, the Talmud stipulates that, even if everyone else is in agreement, the woman must offer consent, and if she withholds consent, the marriage is off. (Bavli T. Kiddushin 2a-b). Likewise, until the middle ages, the wedding ceremony itself was divided into two pieces: kiddushin, the sanctification of the relationship, would take place first. Then, the bride would return to her father’s home (sometimes the groom along with her) until nisuin, the elevation of the relationship, could be conducted several months later.
So, how do these texts help us understand your question?
First, we understand consent to arrive only from communication: true consent can only come if the woman in question understands exactly what’s being asked. This is a vacation for adults; the young lady who loves your son is an adult (well, mostly), so treat her like one. Invite her, but talk through all the implications—including sleeping arrangements. Put everything on the table and allow this ‘smart, wise beyond her years’ woman to make the choices that are right for her.
Second, let’s look at the status of this relationship. You don’t indicate whether your son and his girlfriend are sleeping together or have some kind of shared living arrangement. Nor do you indicate how long they’ve been together, but clearly long enough that you would consider having her tag along with you to the beach (or wherever). That, at least, indicates the seriousness of the relationship. No, they aren’t ready to ‘take their relationship to the next level’, but they are committed to one another. In other words, it’s an adult relationship, so to understand that is to remove the possibility of impropriety. Then again, after discussing it with her, she may decide that the offer is sweet, but not appropriate for her at this time. Only she can answer that. And my guess is, if she is as thoughtful as you say, she'll answer correctly for her--and you.