And Costco now has a nice "super glue" kit.
A dozen tubes or so with a small clear box to keep them protected.
If you are going to make up a kit and have pets - don't forget supplies for them.
Some type of clotting agent.
Hydrogen peroxide to induce vomiting (or the various other chems)
Cuts on the pups foot pads are painful and can make a mess. So once you get the wound dressed you need a way to protect it. Oversized dog booties work well for that, to a degree. You may not stop Rover from pulling the bandage off, but at least you can keep it relatively clean while walking.
Because of my job, our kit is more of a in depth bag of "stuff" I put together. You just don't need a 8000 piece first aid kit that has 3000 aspirins, 4700 alcohol wipes and 6 band aids.
Rite aid, CVS etc. Get a box of standard 3/4 or 1" band aids, some butterfly's, 2" and 4" band aids as well. Maybe even the waterproof type, since the odds are you are out having fun someplace.
A box of 2", 4" and 6" square gauze pads. Couple rolls of "Cling" bandage wrap.
2-4 6x9 trauma pads are a nice addition
Paramedic shears
First aid ointments.
Silvadene for burns if you can get it (Rx). Or other burn sprays. I got three nasty burns on my fingers last year when I grabbed the wrong part of the grill lid. That really hurt. Got a good burn on my leg as well when I bent over the bike to tie it down - wearing shorts.
And there is plenty more if you want-have the room to carry a decent kit.
The real key is to carry it. My kit was packed away for the winter, safe and sound in our basement while we were at the Hatteras rally and Misty ripped a toenail out. What a bloody mess that was - and no kit. Fortunately, fellow Cycloner's the Beasley's came to our rescue.