Interesting Alaska trivia - there are only 4 highways in the state of Alaska!
I've spent quite a bit of time in Alaska for work, so I'm familiar with the state.
The rally route is very do-able, those are all state highways that are in pretty good shape. And the scenery is pretty good on those roads (everyone thinks Alaska is a gorgeous place, but most of it is tundra and pretty flat and featureless. But there aren't any highways on the Tundra, so it's not a problem). The drive north out of Palmer as far as Talkeetna is actually not that pretty and kind of boring. I have not driven north of Talkeetna. The drive from Palmer to Valdez is stunning, at least during the winter, and Valdez is absolutely beautiful.
If you fly and then buy in Alaska, keep in mind that cars are a lot more expensive there, and I wouldn't buy anything older than ten years old. It's a place that can be pretty hard on cars. If it was me driving to Alaska from NY, I'd want a very comfortable vehicle that can eat miles without beating you up. I've never driven TO Alaska, only IN Alaska, but the people I know that have driven there and back have all said the same thing - it takes forever to get there, and you can't really stop and get out of the car to take a break because you'll get eaten alive by the mosquitos the further north you go. Places to stay and eat are few and far between. My sister drove there with her husband and three year daughter in a Corolla, and she said it was the worst thing they ever did. It was a miracle they didn't kill each other, and she didn't want to talk to her spouse for about a week once they made it home. The road can also be really rough, with lots of road construction and big trucks kicking up rocks.
I would also have some realistic expectations about the weather; it can be really wet and cold, even in the summer. It's changes quickly. I've been in Anchorage when it was 77 degrees and sunny, and the next day it was low 50's and pouring.
If it were me, I'd fly there and rent something (also expensive, but cheaper and less hassle than buying and then selling something). You can spend some of the time that you didn't take driving there and see the pretty places in Alaska. You'll see Valdez, and you can go to Denali (if the weather is good, take a scenic flight around the mountain, it's spectacular). If you are into fishing, there's tons of possibilities. If your budget allows, you could fly to Nome for the day (which is long enough, believe me!), or if you want to go north of the Arctic Circle, fly to Kotzebue.
I keep using the word expensive, because everything there IS expensive, and during the summer flights, rental cars, lodging, and food is pricey. Well, it's pricey all the time, but it's worse in the summer because of all the tourists. I'd start making reservations for lodging now, and I'd arrange flights and rental car by March at the latest.
