If Rhae/Daella had a bastard with Dunk and was quickly married off to the Lord of Tarth, do you think Maekar would have known the identity of the father? Fathering a bastard with the daughter of the king seems like it merits death or the Wall at the very least, even for someone like Dunk who was presumably in the good graces of House Targaryen. So it seems like Rhae/Daella might have not told anyone, which is why even though his shield is in Evenfall Hall no one knows about Dunk's connection.
It’s possible Maekar would not have known if Dunk had an affair with Daella (I think Daella for this both because of the nice alliteration and because of Daella’s previous maybe-betrothal to Aegon V). If Daella came to her royal father and confessed that she was pregnant, without naming the father, then Maekar might have, as Cersei suspects Ser Symon Santagar did, found a suitably noble (but otherwise unappealing) lord to take a Targaryen princess-bride quickly - one who would not notice if his wife gave birth to “his” child somewhat sooner than nine months after the wedding - to avoid the scandal of a princess birthing a bastard.
That being said, there still needs to be some reason why Dunk’s shield ends up at Evenfall Hall. It doesn’t make a lot of sense to me if Dunk’s shield is there without Dunk there in some capacity; it just seems random and poised to raise a lot of questions from Lord Tarth and succeeding Tarths. This is why I lean toward Maekar sending Dunk with Daella as her sworn shield when she marries Lord Tarth, with Dunk’s child by her being conceived either before or after the wedding.