I think it all depends on what your fiancee likes to do!
Really isn't it more about making the day special for her than necessarily conquering a mountain? What does *she* like to do? What are the things you guys do together?
If hiking and going the whole day getting tired, hot/sweaty, putting on sunscreen, putting on bug repellant, more sunscreen, taking care of nature calls on a highly travelled trail, dealing with altitude, blisters, possibly getting rained/hailed/snowed on, etc., etc., etc., isn't her cup of tea, just because she climbed Halfdome once isn't going to make this a romantic trip. If a day in the spa at some elegant resort and an wonderous dinner at a five star restaurant followed by a cozy evening back in the hotel room is "her thing", I wouldn't suggest Mt. Whitney.
On the other hand, the very first time I climbed Mt. Whitney way back in the 80's, a member of the group I was with got down on one knee on the summit and proposed to his girlfriend, who gladly accepted. But, hiking is what they did together A LOT. Being out in the mountains together was a common experience that they treasured. That made the moment special for them. It depends on the two of you whether or not this is a place that will hold special significance for you and thus, is worth the effort to do it or not.
I don't remember if your sig says where you're from, but if you were willing to hire a helecopter, you could certainly charter a flight to San Francisco or (if you already are there) to some other elegant locale and blow a bundle on the fanciest restaurant in town. Add details on either end as you see fit. That would be memorable proposal in most ladies books I would think. Someone I heard of once helecoptered to the top of one of the buildings in downtown L.A. and did a similar deal.
p.s. And why are you limiting yourself to a DAY hike? Since you're planning for next year, you could do an overnight hike at least. Take things a little slower, spend the night at Trailcamp, surprise her at the top, and hike back out on day 2...
Just a thought.