There was a thread here where we had a long discussion of how to model "Highlander"-style immortals in a Runequest game. I even had a formula for calculating the skill level of an NPC immortal, with variants for "normal" immortals, vampires, and "highlander" immortals.
I suggest going back and reading that thread for the discussion of ideas.
As for the Quickening, I think what I would do would be to have the quickening immortal make an Improvement Roll for every skill that the slain immortal had less than the quickening immortal, and add the quickening's immortal's POW for every skill that the slain immortal had more than the quickening immortal. The quickening immortal then gains 1 POW if the slain immortal has a lower Power score, 2 POW if the slain immortal has the same Power score, and 3 POW if the slain immortal has a higher Power score.
I am not confident that that is the best way to handle the Quickening, but it's a start. I've only seen about four episodes of the series. My view of Immortals made them very powerful, with the idea that an Immortal would never be a PC (or at least, a PC would never be a "highlander" immortal). So while my PCs might encounter one, they would never be one.
If you want to have "highlander" immortals as PCs, then you have to be more careful about game balance.
(Of course, somebody will point out that in the TV series and the movie, the immortal characters were simply called "immortals", some of whom just happened to be Highlanders. But for this game, I've been using the term "highlander immortals" to differentiate from other immortal characters who do not benefit from the Quickening.
Although, in my own campaign, in which Amazons are immortal but do not go around cutting people's heads off, maybe they could benefit from the Quickening but either don't know it, or have decided not to play that game.)