Physically, you'll most likely be just fine. Start now and climb up (and down!) stairs, don't just go find a stairclimber in the gym. Lots of stairs/week, build up those legs. Start hiking around home, better if you have hills, build up to several miles per trip.
The most physically demanding part of the trip I found was from the parking lot to Camp Muir. Almost a mile elevation gain in about 4 miles of trail, about 1/2 way through sloggy snow.
Now the part where you really want to go with someone who KNOWS what they're doing is glacier travel and reading the weather. Your best bet is to spend the few $$$ and go with a guide service. They're up there all year, and know the snow conditions, the glacier conditions, the trail conditions, are very good at teaching you travel and self-arrest techniques, have medical training, good judgment as to where/when to go/not to go, have SAT phones and two-way radios (real ones, not just the little walkie-talkies you find in the sporting goods stores) in case things wrong, and so on.
If you were out there in the area and could build a rapport with someone you could eventually trust, that might be a good idea, but if you're just going to "go do it", hire a guide. My favorite is International Mountain Guides (
http://www.mountainguides.com/rainier.shtml), based in Ashford. I've used them 4 times (and I started mountain climbing with Rainier, and summited it at 61yrs old). Anyway, that's what I think from personal experience.