Mmmmm....very good question...you are not the only one looking for this kind of furniture :-)

Well in the expensive range you have :

$$$$ KA International (Salwa Road and City Center) for sofa, curtains - they have a very nice collection of fabrics (but minimum cost for 1 m around 180QR...). One solution you take their catalog you choose a sofa you like and you make it in Najma (you can buy 2 meters of fabrics from KA for the pillows)
http://www.ka-international.com/

$$$$ Natuzzi (in the shopping mall in the right side between la cigale and Ramada Signal)sofa, table Italian modern design
http://int.natuzzi.com/

$$$$ Ligne Roset (beginning of Salwa road on the right side after Ramada Signal) sofa, tables, lights...French modern design
http://www.ligneroset.com/

$$$ The One
Landmark Mall 488 86 69
Villaggio Mall 450 77 78
www.theoneplanet.com

$$$ ID Design
The Mall- D ring road 467 87 77
www.iddesignqatar.com

$$$ Singways modern, modern and modern (futurist in some cases)
Villagio Mall
www.singways.net

W-A-W showroom Wood Architectural Works - prices???(never been there but should be pricey)
Airport Road Teyseer Bulding à côté de Q-Post
Tel: 462 07 47
www.waw-qatar.com

$$$ Bois et Chiffons - Ethnic and contemporary style - if you are you looking for something less "cold" than Ligne Roset/Natuzzi and ID design
RdC City Center
http://www.bois-et-chiffons.fr/ANGLAIS/accueil.htm

More for home accessories :

$$$ Zara Home - more for home accessories
Villaggio 413 51 04 / 413 50 63
Landmark 486 30 62
http://www.zarahome.com/shop/worldwide

$$$ Articles A few home furnitures but more for home accessories
Royal plaza- 2nd floor.
413 02 38

And in the not expensive range we have...euh....well :

Home Center
Jaidah Flyover 435 53 00
City Center 483 94 00
Centerpoint 413 19 40
www.homecentre.net.qa

Homes r us
Hyatt Plaza 469 89 99

and hopefully Qatar living (if you are lucky and find someone leaving behind his "The one sofa" or "ID design shelf" :-)

My recommendation : buy a few basics from the 2 last shops Home Center and Homes r us, accessories from The One, Articles, go a week-end in Abu dabi or Dubai with a big empty suitcase and visit Ikea for curtains, accessories... (you can also send staff over in Doha but you have to multiply by 2 the Ikea price because transport is expensive)
Then save some money, sell your Home Center sofa on QL and buy the sofa of your dreams during sales (you can find very good offers during sales)

Good Luck!