Here in Central Illinois, and South, we have fawns born from late March to August. You can find button bucks still running with their does until late spring when they were born late in the summer. I too have seen that. And you are correct: does will push out all the young from the year before when they are about to deliver a new fawn, Both girls and boys.
The good thing about doe fawns not breeding is that by the time the next "season "(rut) comes along, they are much larger, and healthier, and better developed. The year old does will often give birth to twins that first time, a half year later, rather than to a single fawn.
And, both fawns will be nursed properly and be healthy, where a doe bred too early often gives birth to a weak fawn, and may not lactate enough to feed the new fawn. Then, you have a weak doe, and usually a dead fawn. She becomes more susceptible to predators in her weakened condition.
