Not irresponsible at all, in fact you show good judgement in asking the question, which demonstrates a degree of safety which is to be encouraged.
It all depends on how you feel about it, and you will not know until after you do it. So if you have to plan it now I would plan to do the long distances by car but stop off at various places and get checked out and rent a plane and do some local sightseeing. Every small town has an airfield, and a lot of them will have planes to rent. To be honest, flying long distances in the mid west is boring, but there are superb places to see from the air, and these can be done locally.
If you want to do it in the mid west then you should learn there as there are some nasty mountains in that area which might catch you out if your main experience is from flat places like florida.
You can do the touring next time. However that is not the correct answer, just my opinion. I don't know what you are like so have to guess.
Search on this forum for great advice on how to plan a trip in the US.