90 days may not be enough in a raft - lower river is slower, more windy and difficult to navigate. However there are parts of the journey that would be suitable for a raft - canoe better but raft will work. Eagle to Dalton Highway Bridge approaches 600 miles.
The logistics of the trip you describe will be difficult/expensive no matter how you do it. We fly boats in and out regularly - it ain't cheap. You can drive to Eagle but then you've got to get your vehicle back - probably have to fly from take out to Anchorage and then charter/small plane back to Eagle to pick up your rig. Or you can fly in/out with Anchorage as your base - it will cost a bunch. If you have a friend that wants to see Alaska but not float - or float other rivers while you're on the Yukon they could drop you off and pick you up if you choose to shorten your trip to take out at Dalton Highway Bridge.
Consider a mount and small motor - it can get windy, real windy. Camp on bars - bugs will be bad. Bring bear/spray or hand cannon - lots of bears. Look into shipping supplies ahead to Tanana/Galena. If you're a skilled canoeist you might consider renting canoes - probably as cheap as getting your raft up and back.
If you do go as planned it will be an adventure. The links below may help. God Bless and good luck.
- good general description of the river
- well written story of a trip similar to your proposal
Paddling the Yukon River
- good source of information