Since the trailer is most likely its own title/movie on the DVD, a quick and easy way to grab the clip would be to use DVD Shrink.
- Make sure the DVD is not decrypted
- Open the DVD in DVD Shrink
- Select Reauthor mode
- From the Extras branch (most likely), locate the title/trailer you want to use and drag to the DVD Structure window.
- Backup the DVD
- Just demux the VOB file from the Shrink output for a 100% perfect copy of the original clip.
If the clip is combined with others, you can always use a freeware app like Cuttermaran to cut out the specific clip you want from the Shrink output. If you can find the trailer from the original DVD VOBs, you could skip Shrink, and just use Cuttermaran to cut out the trailer. It might involve more searching through the VOBs which would be time consuming, so the Shrink option may be faster in the long run.