That should work.
I assume you are arriving on American Airlines and your daughter will depart on Qatar.
Qatar departs from Terminal D and all flights from FSM yesterday arrived at Terminal E (although the morning flight was cancelled).
Fortunately all terminals in DFW are connected airside by the SkyLink train (https://www.dfwairport.com/guide/connect/) So you can exit the plane with your daughter and use the train to get to Terminal D and walk to her departure gate.
Sometimes there are document check points right at the gate but that varies sometimes even from one day to another. Even if there are, you can just wait right outside the gate check point until it's time to board.
Travel tip: make sure you understand all Covid related requirements to enter Doha and that you have all required document available and ready to present. Sometimes you need to show them every step along the way, sometimes no one wants to see anything at all, you just never know.
A 18-year old should have no problems maneuvering this on her own, especially if you walk her through the process up front. You can sit down with her and look at a terminal map or watch a video together: https://www.youtube.com/watch?v=muxjEz9KFlw
If she is properly prepared she can easily deal with small hiccups herself even if you are not around. My daughter did her first international flight on her own when she was 14 or 15.
Answer to the general question
Are people without boarding passes allowed to see relatives to the air plane gate?
No. Without a boarding pass you will not be allowed into the secure area. Your case is different, since you actually DO have a boarding pass, just not for the same flight. In that case it depends a lot on the specific details, an in particular on the terminal layout. You got lucky since the terminals in DFW have an airside connection.