As a first tour, I rode the TransAmerica this Summer self supported (camping, carrying our own stuff) with my daughter and a friend. It was 4,244 miles in 73 days. I am only 56, but we met plenty of folks older than you doing the same. I plan to be able to do self supported touring well past your age.
An organized supported tour like this should be no big deal. The mileage sounds like something anyone in reasonable health could manage if they prepare for it and put in some training miles. Camping gear is better these days than when you were in your twenties. Do buy a nice sleeping pad, especially if you plan to do much camping beyond this trip. I like Thermarest, but Big Agnes and others make nice ones.
I say that if this sounds like fun by all means go for it. Some people do rides like this at least into their 80's. At 61 you could have many years of touring ahead of you if you want to and stay in reasonable health.
Much of the ability to do a thing like this is the willingness and commitment to do it.