Not intentially can a doe delay coming into estrus or giving birth to any degree. At least not to my knowledge. I have extensive agriculture reproduction background, but not deer in specific.

If the doe is not healthy, it may have estrus delayed, reduce the number of eggs ovulated or may not come into estrus at all. The body's priorities are remaining alive and growing into maturity. After that, energy will be spent for reproduction and other physiological items. So if the deer is in really poor physical condition, it will not spend it's limited energy for reproduction. If the doe is healthy, hormones will controll the estrus process and the deer itself will not be able to control them any more then a woman can control her ovulation time or menustration cycle. Almost all mamals lack the capacity to store semen as well, so fertilization of the egg must occur within a few hours of mating if it will occur at all.

As far as the birthing process is concern, the fetus actually signals the start of the process. After the process has start, the doe itself can delay birthing by only a few hours at the most.