Re working in a common area and not taking electronics to private areas like bedrooms - this is recommended in every Internet safety talk I've attended.
QFT.
DD is terrible at self-regulating her TIME on this kind of device, and rebels continously at our attempts to do so, quite frankly. You know your child best, but my strong recommendation is to get her a set of earbuds and tell her that this is her "privacy" for writing, and then create a family AUP and have everyone SIGN IT.
DD14 does NOT use a laptop in her bedroom, and if she is trying to use one where we are NOT... (that is, if she moves to her laptop in the loft if I'm downstairs... and moves to the downstairs desktop if I'm up here on my laptop) then I know that she's probably doing things that she shouldn't. Not usually that she's doing inappropriate things-- just-- that she wants to use the technology to do things that aren't authorized at the time.
Our general rules are:
a) we hold ALL passwords. Period. If she has an account somewhere-- we know the url and the password. Period. Any violation is an immediate loss of privileges, regardless of the consequences to her or to us.
b) we spot check her computer and her activities online. This is a shared parental responsibility. DH is the FB guy, and I'm the Tumblr, DA, message board, and school one.
c) NO private use of web-enabled devices for internet activities. For anyone. As adults, we bend this rule enough to check out/purchase books with our Nooks or phones, but the rules are different for kids.
I second the recommendation of a Chromebook, or maybe another netbook. It's keyboard-ey enough for serious writing, but will run a lot of the fun apps and is more portable than a laptop.