Yes rent a car. Book it early as they're sometimes scarce from all the tourists. It won't be cheap, ask if there's a limit on the miles, sometimes they're extra.
You might skip Girdwood, but that would make Byers Lake/Denali to Seward a long day. There's not a lot to see in Girdwood, but the ski tram should be running to the top of ski slopes for nice pictures if it's a good day. If you do stay in Girdwood, taking the tunnel through to Whittier is interesting (I don't know the cost) and then you'll have time to stop at the Boggs Visitor Center at the Portage Glacier. I believe there should be some road side boondocking spots on the way into Boggs.
Bill