If your sod appears to have taken hold, then go for it! But first put down a pre-emergent so the existing crabgrass seeds (and the seeds the birds poop in your yard) don't take hold. I'm assuming that since you've cut it a few times, it's considered established. There are quite a few companies that make selective herbicides for nutsedge. Image and Sedghammer are two that I know of. But I've also heard that Horticultural Dry Molasses is an effective organic method.

Fertilizer is a good idea as well for you new lawn.

Here is a link that might be useful: Molasses sedge control

if crabgrass is growing now it is too late for a pre emergent which needs to be put down several weeks before the seeds start to germinate. Every post germination crabgrass control I have used also killed any nearby grass that poison contacted, so most often I will pull any crabgrass I see growing or try to keep the plants from producing seeds.