The way I see it, you've written yourself into a corner. I'll try to break my reasoning down here, and come at this from different angles to show you why I come to that conclusion.
First.
Dragons, in Medieval times, are seen as beasts to be slayed. Adventurers, in the traditional fantasy sense, are in it for money, glory, or for the thrill of the hunt (for generalized archetypes with the group). So, what part of this won't attract adventurers in droves?
To get around this, you would need a reasoning why dragons are so feared, few would dare face it. And that creates a new issue, because you need people to face it regularly enough to feed it. Adding that it was common to have hunting trophies hung so that local lords could tell the epic tale of how he felled so mighty a beast. So you add to the issue.
Second.
'To rescue his daughter'. Rescuing a princess is often equated with earning her hand in marriage. Even if not outright stated, it is often assumed. And that would attract nobles in droves itching to climb the political ladder. Or does marrying a princess mean nothing in this setting?
Even if it doesn't include a claim to inheriting the throne from the king, which many would argue marrying the princess does, it comes with clout. That's what political marriage did in time period. The mere mention of a princess in peril will drive most if not all single nobles to act.
To further highlight this. There's the simple act of 'saving a damsel in distress'. All you would need is one man with a hero complex and an army under his command, and the king's plan is ruined. 412
While it can be argued most would be more pragmatic about it, claiming that no one would is patently misguided.
Third.
Even if you have the king issue decrees to the nobles not to engage the dragon, which comes with a slew of issues in and of itself. And even if you ignore my first two points entirely. You have one very important hurdle to overcome: the common folk.
What happens when there's talk of a wolf lurking too close to their herd? They panic and try to band together to hire someone to take care of it, if not hunt the beast themselves.
Now there's talk of a dragon? It can be argued that most will not pay it any mind as long as this dragon stays far away from their farms and herds and families. Until, that is, a single incident that cannot be readily explained otherwise. Perhaps someone falls ill and they don't know the cause of the illness. Or someone goes missing and can't be found or, worse, a half-eaten corpse that might be the missing party is found.
All they need is one person in an angry mob to suspect this dragon and give voice to it. And you've got yourself a brand new issue on your hands. So now there's not just adventurers to contend with, but local militia out for the dragon's head. They might not know or even care about the reward, they just want revenge.
While it can be argued that common folk stand no chance against a dragon, will every farmer refuse to face a dragon when farmers were so often drafted into the military to fight a noble's war? It would just take one such a survivor to take up arms. And given how many peasant revolts took place in history...?
Conclusion:
Your best bet is to use this dragon as your executioner. Have the king make a new decree. That anyone who commits a crime that warrants it, the perpetrator will be fed to the dragon. Depending on the population and prosperity of the kingdom, it would happen often enough that you should feed it regularly enough.
But it still doesn't negate the above points. The king would have to play his cards carefully. Admit the dragon is in the kingdom's best interest and rival kingdoms will hire adventurers to slay it, in order to weaken them. Admit to nothing and people will get nervous about tales of a dragon.
Given massacres have been sparked by 'cruelty to a cracker', I do not have high hopes this will work out in the king's or the kingdom's favour. 164