Good idea
I’ve only done this once, but it works well. I think I used slices maybe up to half a centimeter thick or slightly thinner (whatever that equates to in inches or whatever measurement you use). I dried mine in the oven, very low setting about 80 degrees celsius, and started with about and hour (check them halfway and it can help to turn them). I can’t remember what lengths of time I used but for some things I found an hour was plenty, other things needed longer. Many things will continue to dry and harden up once you’ve removed them from the oven, so they don’t need to be completely crispy before you remove them, if that makes sense. I’m sorry I can’t give more detail, it was probably a year ago that I last dried carrot.
In terms of feeding, treat it exactly the same as fresh carrot in treat amounts (1 small slice daily max), the only thing removed from them is water, so even though the pieces are smaller, they have the same amount of sugar etc as a fresh piece before they were dried. I think a lot of people accidentally overfeed dried fruits etc because of this, so just take it easy 