Others have already covered the specifics and skills needed to shoot a 1000 yards at game animals so I want talk about that except to say, If you are going to take any animal larger than a ground hog at distances out to a thousand yards ethically there are only a hand full of cartridges out there capable of doing it in less than a second and delivering enough energy to get the job done right and none of them will be fun to shoot or very accurate in a 6lbs gun. IMHO. They are 26 Nosler, 28 Nosler, 7SAUM, 7mm Remington Mag, 300 Win Mag, 300 Weatherby, 30-378 WBY, 300 Norma Mag, 338-378 Weatherby, 338 Lapua and any of the RUM mags (7mm, 300, 338). I am sure there are others but you get the point. The SAUM, Rem Mag and Win Mag are negligible at that distance but would be my minimums.
As far as the rifle goes I am not aware of any factory offerings in those calibers under 6lbs. If money is no matter? I would build a full on custom with a carbon fiber barrel. It is about the only way to get there. The Sako 85 carbon lite is an excellent rifle but I don't think it is available in a magnum cartridge. Terminus and Curtis build some light weight actions. You might start there.
As far as the scope goes? Leupold VX5HD CDS 3-15x44 with HTMR reticle if you can find one.