Well I don’t have a child the age of yours interested in weaving but I am a weaver myself so thought I would give you what I know about looms.
At mentioned in a previous post, potholders are normally done on a different type of loom than purses or scarves. In my opionion a potholder loom is one of the easiest and cheapest for a child to start on. This is the type of loom I learned to weave on at 6. She should easily be able to handle this type of loom.
The Harrisville Peg loom is a tapestry loom and she would be able to use it to make small items (purses, pillows, wall hangings). It works on the same principle as the pot holder loom only using yarn instead of the loops. I see that it is rated for age 7 but personally I don’t think it is any harder to use than the pot holder loom. I have one of these myself but do not use it since I find my rigid heddle loom much easier to use.
The next step up would be a rigid heddle loom. These are the most versatile of the looms mentioned and could be used for the purses, etc as well as longer items such as scarves. You mentioned the Harrisville Easy Weaver. Others small ones would be the Beka Rigid Heddle Loom and the Schact Cricket. This type of loom would be harder for a child to warp (putting the lengthwise strings on the loom – you may end up doing that for her for a while) but much easier for her to actually weave with. My personnal preferance for ease of weaving of the three listed would be the Schact Cricket but it is also the most expensive.
You can find any of these looms online at http://www.halcyonyarn.com.
Personally I would get a potholder loom and let her try it. If she really enjoys it and wants to do more then I would upgrade to a rigid heddle type loom.
Hope this helps.
Schele