Why would your niece want a 15 inch or larger screen laptop. These are super heavy at 2.5 kg or more. Try something with a smaller screen and sub-1.5 kg. It's much easier for her to carry it around.
I recommend the ASUS UX-305UA. Core M processor, 4GB RAM, 128 GB SSD, 13.3 inch full HD matte screen. $1098 for this spec. Probably can bargain a bit.
Let me explain why I recommend this laptop. I bought one for my friend as well. This laptop is only 1.3 cm thick and weighs only 1.2 kg. Super light and super thin. It's also completely silent as it does not come with a cooling fan. The Core M processor runs so cool it doesn't need a fan. Also it can easily give you 8 hours of battery life under balanced power settings. The touch pad is superbly responsive. The matte screen makes looking at the screen for long hours much easier cos there are very few spots of reflection.
Finally, if you really need a big screen, by a cheap 23 inch AOS IPS screen at less than $250 and hook up the laptop, add a wireless keyboard and mouse for $35 from Logitech and you're good to go. That's how I do it at work.
Yes this combo may cost a bit more than your $1000 budget but hey it's both extremely portable and can function effortlessly as a desktop at home.
The laptop's specs are more than sufficient for her homework which probably would consist mainly of email, social media, surfing the internet, Office productivity, maybe even some Photoshop use and some simple video editing if necessary. I've tried all these on the laptop and it just flies through everything except video editing (I just clipped videos using VLC).
