Keep in mind that a motivated dog can:
(A) Move a helluva lot quicker than any human
(B) Dish out tremendous punishment in short order
(C) Hard to hit when they are covering ground as quickly
(D) Absorb a lot of punishment - more, it seems at times than a human
Caliber WILL matter on a large, fast moving, highly motivated dog; just as much as will placement. I don't know how many here work with dogs but they are extremely quick. It boggles the mind to see something the size of a Rottweiler 'drop it in gear' and cover ground at what appears to be twice the rate of a highly trained athlete. IFF (if and only if) it has targeted you as "IT" you'll have only one shot (pun intended) and he's got a hold on you.
I cannot put a large enough exclamation on this: CARRY AN ADEQUATE PISTOL. TRAIN Proper "Point" Shooting as well as Surgical Speed Shooting because that's just what it's going to be (assuming you have a date with a highly motivated Rottie, American Bulldog or German Shepherd).
If you "cannot" deal with this advice then run at a local High School Track.
Pepper spray also works well (iff you are upwind of the beast) - I'd always carry this. It's on my bicycles and I carry it - especially when I choose to go walking. It gives me a less than lethal option.
An aside: Here in SE Michigan an elderly couple was mauled to death by a pack of American Bulldogs. I think it was primarily two but another was involved. Your Derringer/micropistol would not serve you well.
A fighting blade is comforting but you'll take a bite to use it. But you may take a bite anyway...
Several support your claim that you cannot run with a pistol in FL in the summer. I disagree: J Frame and fanny pack. I know because I'm from South Louisiana. I ran track in HS and I still jog (though mostly I do track workouts on a track).
As for the "11 + 1 .45 ACP pistol"; well, that's ridiculous. No one advocated a full-sized service pistol...
".22LR in your breast pocket is better than the (I'll say 1911) in the car..." I will call BS on this one. You SHOULD have brought the (I'll say 1911 though it could be the M&P, Glock, Sig, XD...) the PROPER tool for the job and the job is engaging several highly motivated persons or a highly motivated Presa Canario or Fila Brasilero. To me that would be a full-sized pistol and a solid fighting blade on the weak side.
Look, I know everyone is unique and what is "adequate" for some is "too much" for some and "inferior" for others. Carry what you wish. If you're comfortable then go with it. However, expect "heated" discussions as to the logic by others who feel haat micro/mouse pistols have no place in their collections.
"Necessity is the plea of every infringement of human freedom. It is the argument of tyrants, it is the creed of slaves." ~ William Pitt, 1783