I did a half on 5/7, one on 5/21, and am planning one for 6/11. I try to do at least 1 10k or longer race per month.
That said, as a new or newer runner, or a lower mileage runner, be careful in planning too many race close together or that much of a ramp that close together. For you, a fall race sounds completely reasonable - - but be sure to plan for rest and recovery time in between races.