there's no real answer to this - because it varies from person to person. If i started pushing myself my body would go into shock, because apart from having a fairly active job, i'm not at all active. however, if you say, walk to work every day and run around after kids in the evenings, your body will be used to exertion.
i would advise doing two things. firstly, tell your trainer exactly what you've been eating. explain you are committed to the plan and won't be changing, (if s/he tried to persuade you, say your doctor has advised it) but that you want to exercise safely within that diet.
secondly - listen to your body! if you feel exhausted, or light-headed, or you start aching more than you would expect, maybe you're doing too much.