This loosely meets this forums criteria but Flash is a much less aggressive program on a laptop than After Effects. AE will eat a quad hex workstation with 128GB RAM and make it cry for its mama.

RAM is going to be essential to keep you operating as well as a discreet video card.

Laptops in that price range typically come with integrated video cards and 6GB ram or so. You want 8GB minimum as just Photoshop (assuming you use this too) will happily gobble up as much as 50% system RAM. AE + PS + Flash makes 8GB the bare minimum. Just AE, to be honest, makes 8GB the minimum. If you even think about enabling multicore processing you'll need to dedicate, for safety, at least 1.5GB per core. They're all quad core so at 4 cores that's already 6GB, not including the RAM the OS needs or anything else. Besides, I'd probably never enable multicore processing on a laptop. It will use all the cores anyhow, just slightly less efficient, very slightly.

The video card is the next biggest concern. The problem is if you buy an integrated video card like the Intel HD 2000-4000 series that typically comes on i3/i5/i7 laptops then you share your system RAM with your video card. So consider up to 2GB system RAM to be required for the video card. So a 8GB laptop becomes a 6GB laptop just that fast. So what you want is a laptop with a discreet (separate) video card like a GeForce M or Radeon HD Mobility. They have their own RAM (usually 1GB in that range) and won't bother your system memory, as well as vastly outperform Intel HD graphics when using adaptive or openGL rendering in AE.

As for Flash, it's pretty happy in an environment. Lately I wouldn't have less than 6GB just to have it as even with 16GB I sometimes get "out of memory" errors exporting heavy library projects. I chalk this up to a mem leak in Flash (CS5.5 for me) more than the lack of RAM though as I restart Flash and it's fine again.

All that said, considering their speed, warranty with willingness to service on-location and technical support overall, I'd point you to a Dell Inspiron (or better). http://www.dell.com . I've always been extremely happy with their offerings and have many servers, laptops and LCD monitors from them over the years.

I realize this is $899 but hey it still starts with 8 . This would be easy to carry and sit on  your lap but do note the screen is not full HD. It does have a modern processor, 8gb ram and a discreet video card however. It would be very peppy:

http://configure.us.dell.com/dellstore/config.aspx?oc=fncww03&model_id =xps-15z&c=us&l=en&s=dhs&cs=19

Personally, for something you'd use to make money and would want to hang on to for a long time I'd spend the extra couple hundred, upgrade to a 17.3" screen full HD 1080p if you plan on working on HD video, still with 8gb ram and discreet video:

http://configure.us.dell.com/dellstore/config.aspx?oc=dncwn13b&model_i d=inspiron-17r-se-7720&c=us&l=en&s=dhs&cs=19