Rt 1 from Miami to Florida City is congested with no shoulders and not very wide outside lanes so will have a close interaction with traffic.A better choice is Old Cutler Rd. picking up back roads east of Rt1 on into Fl. City.
At that point you have a choice of Rt1 or Card Sound Rd.Rt1 has a wide shoulder but with rumble/snooze bumps that are irratating plus the traffic is particularly fast on this desolate stretch to Key Largo.Card Sound Rd. is generally more popular with cyclists due to less traffic even though the first 10-15 miles can have periodic cement/gravel trucks from nearby operations.It adds about 15 or so miles to the route and has no shoulder but takes you though a remote scenic undeveloped area of the Keys (w/o much in the way of services-one bar/grill I think)which can be particularly buggy especially during the wet season.
Once in Key Largo the development/tourism and services start again and on to Key West the shoulder along Rt1 is generally adequate the whole way with one or two manageable exceptions.As well there is a bike path being developed along this stretch l which is an option but seems more dangerous to me ,in crossing intersections and running on the wrong side of the road etc.,so I prefer to simply stay on the road/shoulder.For specifics on the route and services check this link:
http://www.floridabicycle.org/messen.../winter038.htm
but overall in Fl. City there are motels,services and a nice hostel then services are slim to nonexistant between there and Key Largo where many campground and motel options pick up and options are adequate all the way to Key West though they can be quite expensive and booked in season or spring break.There is also a hostel in Key West but it doesn't get as much favorable feedback as the Everglades hostel in Fl. City.