In a fight with Kira, Dukat would lose...
In the episode, Kira makes it very clear that she will kill Dukat if he harms Ziyal in any way. Given Kira's ferocity and the fact that she has killed actual Cardassian soldiers in the past (something Dukat is well aware of), she likely thinks the threat alone is enough to keep Dukat in check.
KIRA: There's no way I'm leaving you alone here.
DUKAT: Well, then I suggest we devise a plan to rescue these prisoners together. You need me, Major.
KIRA: Maybe I do. But if you hurt that girl, I promise I'll kill you.
While they didn't have this particular conversation until they discovered the survivors, Kira was clearly always willing from the outset to use deadly force to stop Dukat, and believes she can indeed stop him. Hence, from her point of view, it is not necessary for her to detain Dukat, especially given his potential usefulness for the mission.
Also note that the Cardassian Union contacted the Federation and Starfleet before Kira left for the search insisting that a Cardassian representative chaperone Kira on her mission. From Memory Alpha:
While Kira prepares for her departure from the station, Captain Sisko drops in on her and asks Kira to put off her departure, as the Cardassians have asked to send someone along with Kira. She tells Sisko that she'll wait two days, and not a minute more, before she leaves.
A little later:
When Sisko makes it back to Ops, he's told by Worf that the Cardassians want to beam someone directly into Ops — someone who turns out to be Dukat. It seems that he is the one who's to accompany Kira on her search for the Ravinok, and he too is anxious to leave.
Putting the facts together...
- Kira must take a Cardassian with her
- Kira wants to leave for the search as soon as possible
- The Cardassian assigned is Dukat — she could petition through government channels for a change, but this would take time (and may result in nothing)
- Dukat reveals that Tora Ziyal, one of the potential survivors, is his daughter, who he will terminate if he finds her
- Kira is rightly shocked and sickened, but (a) she knows she can disable Dukat if necessary (her fighting skills are superior), (b) she has been ordered to let Dukat accompany her everywhere on the mission, and (c) they are about to infiltrate a Breen prison camp and two people are better than one for a mission with this level of danger
- Given her reputation, she likely believes that the threat alone of killing Dukat in retaliation for harming Ziyal is enough to keep him in line