Certainly not familiar with your warm and dry climate, but only way to do that here in mn is to plant alfalfa with the oats.
You get a moderate cutting that fall of alfalfa, or if you cut the oats before it heads out as hay, you may get 2 cuttings of alfalfa. The following 3 years are the money makers.
Again, 'here' its difficult to plant anything in late June as its too dry to get hay type crops to root in.
If you get lucky here, the harvested oats will regrow from the light seeds that blow through the combine and will give a cutting of oats hay by fall?
Planting times here are until the first week of June, and again in the last half of August. Doesn't often pay to plant anything in between, too dry too hot. Don't know what your climate allows.