Sure, it's possible. You'll have to convert the files to a format compliant with iTunes/Ipod.
I have the same Ipod and I use retail software...all of it from Fab.
All the software is available as 30 day free trials so you won't have to purchase anything, at least not for 30 days and then only if you decide to keep it.
There are other softwares and other members can lend their expertise with them.
This would be mpeg-4 or h.264 iTunes compliant profiles.
1). Download or transfer the episodes of the series to your hdd.
Yes, you can do this from the disc, but it'll be smoother from the hdd and won't take much time.
The actual conversions will take longer and are much more of a load on her cpu
2). Open each file with DVDFab Mobile, choose Ipod for a device and then choose one of the 2 device profiles I listed above.
Then convert it. You can batch these files, but let's not go there now.
I'd leave it on default settings for starters.
You can convert just a chapter or two as a test and view the video on her pc to see what settings she prefers.
There is also a profile called Ipod TV Out, but I've never been a fan of it.
This can get quite complicated, but hopefully won't.
The tv recordings will be in DVD-VR format which, strictly speaking, is not compliant with your typical dvd, ie, it does not conform and does not contain VIDEO_TS and AUDIO_TS folders and won't play on some dvd players.
Having said this, Fab Mobile should have no problem recognizing the DVD-VR format and once it's converted, your daughter should be all set.
Just drag and drop it into iTunes and sync her Ipod.
If you choose this method and run into trouble, post a thread over on the cdf Fab subforum and we can help you with this software.
There are other perfectly good methods to do this.
Best of luck to you and your daughter.
Oops, forgot to post a link: