Since you have the navigator and pirate (instead of just one of those), you are guaranteed to get Queen unless 1) you are unattentive, 2) he moves into the fog of war, or 3) she hires a pirate to counter your Queen hunter.
If you won't be online at the time of arrival, just navigate to an outpost so that the travel path will be close to the outpost with the Queen, so if he does move her, you can capture her mid flight.
Conclusion: Queen hunter combos don't need any drillers to get a Queen, unless 1) you want to reuse the queen hunter or 2) enemy has a pirate with drillers to take out your queen hunter
Reporting from the Bridge