Landing in Terminal 1, taking off one hour later from Terminal 3. With only a one hour layover, will I have enough time to change terminals?
DFW does not use numbers for terminals. DFW uses letters. So....
Presuming you mean Terminal A to Terminal C, yes. If, almost certainly, American Airlines sold that itinerary as a single ticket, they expect you to make it and from experience, yes, it is enough time.
As soon as you enter the terminal, look for the SkyTrain signs. Terminal C is the next terminal in the inner loop.
If you require mobility assistance, you can arrange that prior to departing for DFW.