yes you will need an active converter. the 1xxx series cards do not have DACs (digital to audio converter) onboard any more. the result is that you will need an active converter. that looks to be right but I suggest you get a unit that is powered by USB like so.
https://sgcdn.startech.com/005329/media/products/gallery_large/DVI2VGAE.D.jpg
from the page the resolution you listed is not on the supported list
"2. PC resolution supported: 800x600, 1024x768, 1280x768, 1280x800, 1280x960, 1280x1024, 1440x900, 1600x1200, 1680x1050 @60Hz, 1920x1080 @60Hz, 1920x1200 @60Hz"
I do not know if that means it will not work or if it will, be aware.