I presume your daughter won't be talking for hours per day on Skype, so I don't think the particular headset choice is that big of a deal. I travel light, and so I just have audiophones that stick in my ear with a microphone built into the cord (for my netbook), the quality is fine.
Now that I have traveled a lot using Skype all over the world, I am more negative on using it to call back home.
The elephant in the room is just using Skype in general, it is a pain to have to make calls only when you have a WiFi connection or internet AND you have your computer running. Same goes for receiving calls.
I have also tested the Iphone Skype app (on my Ipod Touch) and it had decent quality. But anything over Wifi is not as good as a regular phone connection, and you can't text or check voicemail from the Iphone/Ipod Skype application.
Based on my experience, my suggestion is to have your daughter get a calling card and use her mobile to call home. It is way more convenient, you can call from anywhere, and with higher quality. I call the USA from Thailand for less than 3 cents per minute, including all charges. I am sure there is something similar in England. In fact, one can call Thailand from a landline in California for only 2 cents per minute by dialing a 5 digit code first! So research these possibilities.
When I was in living in the country of Colombia recently, I would usually end up paying 13 cents per minute on my mobile phone to call the USA instead of FREE on Skype because it was so much more convenient and the quality was much better.
Also, Skype is convenient for call forwarding, if you want it. Anyone can call my USA phone number and I was forwarding the calls to my Colombia mobile phone, the quality was very decent. If you are on the East coast, she may want to consider this, also (the time difference being less). When I am in Asia, I don't forward calls due to the time difference.
Kramer