I see major issues with this idea.
Medrunner Lao Dorn and his team have been given a mission. A young woman has contracted some sort of parasite that is slowly eating away at her vital organs. The parasite is of unknown origin and the doctor's on Oberon are unable to treat her.
Rule one : quarantine.
Absolutely no one is going to transfer this woman (or anyone on Oberon) to another place. People and supplies might be sent down, but nothing going down is coming back until the outbreak is identified and a cure available.
Any other approach risks infecting the entire solar system with a potentially deadly plague.
Only freezing her will stop said parasite (the specifics of the parasite would be a later question).
If they can freeze her, what's the rush ?
Only the doctor's on Venus might be able to treat this woman. Lao has been tasked with getting to Venus as fast as possible so the woman can be put under the care of Providence.
Remember quarantine. This trip to Venus is not going to happen.
What kinda propulsion device would allow Lao's craft to reach Venus from Oberon in approximately 1-2 weeks real time (not Lao's possibly dilated time)
"kinda" is not good grammar - use "kind of" instead. :-)
Entirely depends on where they are relative to one another - planets and moons move.
The question arises as to how many other people would be affected by an unknown parasite by the time they arrived ? Likewise it's hard to see how they could tell who is in the early stages of infection and who is not ?
There's no way to know for sure and that's why you quarantine.
Note : fusion power is available Medrunners are publicly funded so expense isn't an issue unless it's ridiculous
"Fusion" doesn't mean much. Just because I can do fusion that doesn't tell me anything about mass requirements, fuel requirements, propellant requirements (and you still need propellant) and issues like acceleration limits and life support requirements. It's a medical ship which adds other complications.
Expense may not be an option, but preventing the spread of an unknown and probably lethal parasite certainly is an option. This is the reason you're going to have a quarantine imposed. It would be a hard quarantine and the ships you''ll be rushing there will be ones that can destroy any ship attempting to break out of the quarantine.
Best case scenario : a quarantine facility or a facility capable of being erected on Oberon rapidily (prefab ?) is going to brought there with medical staff on a one way trip.
So the minimum period to travel would be something around 12 days according to the calculator page provided by @Morris-the-cat in comment. But that omits the time to make decisions and plan and provision the required outfit. Politics may delay things.
And that's going to be more likely a range of 5 to 30 days for a quarantine fleet to arrive at different times around Oberon. They'll be dispatched from different places within the solar system on an emergency basis and provision for ongoing maintenance of the quarantine zone would develop over time. It would be perhaps two or three months before the quarantine system was fully in place.
But lets remember there is another option : wipe out the colony from space. Why waste money on this and take the risk of a breach of quarantine when some relatively simple kinetic weapons can wipe out the problem from orbit ?
The priority here will not be one persons life, or even the life of the colony. It will be the life of the rest of the solar system.