New grass can be easily damaged by weed killer application.  The general “rule of thumb” is to wait until the new grass has been mowed 4 times.  Unfortunately this puts the application right in the hottest driest part of summer.  Weed killer will not want to be used on a lawn that is dry or when temperatures are expected to be above 85° to 90° or it will kill the grass as well as weeds.  The best approach would be to use a liquid weed killer sprayed onto each weed and not on the surrounding grass.  This also needs to be done when the lawn is well hydrated and temperatures aren’t too high.  Weed killer is absorbed through the leaves of the weeds so liquid weed killers used this way are usually more effective than granular weed killer.  Lawns also should not be fed during the hot dry days of summer when they are under stress.  If you want to use a weed and feed granular product, you’ll want to wait for late August or early  September when rain returns and the soil is cooler.