If I've saturated and area with weed killer, am I unable to plant?

You will have to wait until the weed killer is totally absorbed in to the ground to plant anything.

What kind of weed killer did you use and how long ago? I would turn over the soil adding in a lot of fresh new soil and amendment geared to what you want to plant there next. Then place landscape fabric down so you do not have to deal with as many weeds in the future. Then mulch.

It should say on the packet what type of weedkiller you've used and how long it takes to dissipate and whether it sinks into the soil.

I agree with Christina. Check the product label to find out the wait time.

you could always go with some raised beds with fresh soil...

Usually not this year unless you replace the soil