A DAC is a Digital-to-Analogue Converter. Technically, if you're listening to digital music (CDs, MP3, AAC, etc), you ALWAYS need a DAC, but the good news is that most sources include a DAC... any portable with a headphone jack such as an iPod or Walkman CD player, most modern computers have DACs built-in to their motherboard, etc.
The DAC built-in to an iPod is already of pretty good quality. I use my iPod Video (old model) with my AKGs all the time. You could plug the Q701 directly into an iPod headphone jack and get plenty of volume. However, from experience, having enough volume(voltage?) isn't the same as having a more refined amp and enough current, and without an extra amp the Q701 sounds only a little better than iBuds, bass and mids don't hit firmly and sound thin while treble will more often sound peaky and irritating. What I do, is I have a cheap Line-Out Dock Connector (FiiO L11, about $11, gets the analogue audio directly out from the iPod's DAC) connected to an external amp (not sure about a cheap one, I guess the FiiO E11 gets my best recommendation for as cheap as I'd bother with, or more expensive amps), which then connects to the Q701. With a better amp, the headphones sound more solid and add weight to the bass and mids, everything (and importantly Treble) becomes more controlled, and the presentation of details and soundstage become more apparent.
Headphones (and songs at least 128 Kbps AAC, higher of course is better with decreasing gains, 256-320 AAC is a good sweet-spot) make the most difference, amps make a little less but eventually you'll need more power to mate up with the headphone, and DACs do make a little difference in resolution and FWIR sweetness of presentation, but a DAC is the last thing I'd worry about upgrading unless the one you have is complete cheap garbage (most PC motherboard built-in DACs, especially cheap laptops and netbooks). All the above is subject to diminishing returns as you spend more, you'll have to decide your own "sweet spot" for cost Vs. value.
IMO, for a gamer, especially if you have console and PC, having a kit consisting of Q701, FiiO E11 or better yet E09k desktop amp, and Creative Sound Blaster Recon3D USB (the USB model that can process surround sound for BOTH PC and console, including all necessary cables) represents high value and is very impressive, you wouldn't be compelled to spend more unless you'd rather spend your hobby money on testing equipment than buying new games.