I personally have only seen Aiptek cameras in stores and I have not used it for any period of time, therefore I cannot give you my personal experience. I am only suggesting this on the basis of value (especially as a "first camera" for a "young person" (I hate calling them "children" because they grow up so quickly nowadays!!))
Currently there are only a few good hybrid cameras that take decent still pictures AND digital videos. All digital cameras now have "video mode", but most of them use a format called MJPEG, which takes up a lot of memory for a small video of poor to decent quality (eg. slow framerate, low resolution). Aiptek and many non-mainstream brands like Mustek, DXG, and lesser camera brandnames like Sanyo, pioneer into newer MPEG4 formats (eg. QuickTime MOV, MP4, Windows ASF) which make decent ot good video with small filesizes (ie. higher data compression). I think Kodak is also following suit into MPEG4 video.
Unfortunately, all the "mainstream" brand cameras easily cost $200+ - my favorite is the Sanyo Xacti series: VPC-C5, C6 and C40, which now sells for as low as about $300, maybe less if you venture into ebay and foreign sellers (but no warranty and any form of guarantee!). Sanyo is not a popular brand in North America, so most likely you can't find them in major retail stores and have to buy it online.
The Sanyo Xactis are _small_ , have good optical zoom lens (C40 having the highest zoom power), good still picture quality (C40 = 4 megapixel (MP), C5 = 5 MP, C6 = 6 MP; C6 has the best picture quality), decent to good video quality (and most likely superior to Aiptek and other non-mainstream brands because of better optical lens; C6 makes the best video in dim lighting). The build quality is also better than the non-mainstream cameras. Another advantage with the Sanyo is that the zoom lens can be operated during video filming, unlike most other digital cameras using video mode. Read Steve's review on some of the Sanyo Xacti models:
http://www.steves-digicams.com/2005_reviews/c5.html
http://www.steves-digicams.com/2006_reviews/c6.html
I don't know how careful your daughter treats her camera, but you know kids are always forgetting and losing things, or banging them around. Maybe your daughter is a very mature and responsible 10 year old who deserves a better and more expensive camera for her tender age.
In any case, the new Aiptek DV6 has 3X optical zoom lens and costs $199.99. With an optical zoom lens, maybe it can now compete with the mainstream hybrid cameras. However, there is no user review yet.
Another hybrid camera I can think of is the Sony DSC-M1 and M2 - but these are VERY EXPENSIVE cameras ($500+) and the video quality is not good.