Any laptop with HD3000/4000 IGPU can handle FHD. You need to make sure the connecting port (VGA, HDMI, DisplayPort ... ) are available at both the laptop / tablet and your secondary output though

Acer
V5-473PG-54204G50, i5-4200 + Nvidia GT740M +(1366x768;touch)@RM2299, 4GB, 500GB,W8 *no OD (at ~ 2kg, not really that light)
V5-132P-3322Y6G50b, i3-3229Y + Intel HD4000 + (1366x768)@RM1799, 6GB, 500GB, W8 (Have to swap HDD to SSD aftermarket)
V5-171-53312G50s, i5-3317U + Intel HD4000@RM1799, 2GB, 500GB, W8 (Have to swap HDD to SSD aftermarket)
P3-171-3322Y2G06, i3-3322y + Intel HD + 60GB SSD + (1366x768 IPS;touch)@RM1999, 2GB, W8 (SSD is small and not easy to upgrade aftermarket)
Dell
Vostro 5460, i5-3337U + Nvidia GT630M + (32GB mSATA SSD + 500GB(5400rpm))@RM2199[1.54kg], 4GB, W8SL, 3 cell (running time on battery is not long. Have to swap HDD to SSD aftermarket).
Samsung
Series 7 Ultra, i5-3337U + Intel HD4000 + 128GB SSD + (1920x1080; anti-glare)@RM2999[JBL][1.46kg], 4GB, W8 (over your budget)
ATIV Smart, Z2760 + Intel GMA + (1366x768; touch) + 64GB SSD@RM2499[774g w/o keyboard], 2GB, stylus, W8 (It's on Atom, SSD is small and not easy to upgrade aftermarket)
Prices are RSP, negotiable.
Thank you for your recommendation. After much consideration, I think Dell XPS would suit my needs. Do you have any knowledge in terms of its battery life of XPS 13 vs XPS 14? Also, any pros and cons in between XPS 13 vs XPS 14? Thank you.