You can keep the insect eggs in plastic bags and store at -20 to -40°C. If you want to store more than 6 months, you can store at -60°C. For a very short time (1-2 weeks), you can store -8 to -20°C.
Nice planning for your study and do corroborate with answer of #Monjurul Haq.
But for your study, I would also like to suggest if you can perform your assessment as soon as you get them in your hand rather than storing them as 'undone/ to be done target'. Because, any stored organic part or portion wont be as reliable as the natural ones, you simply cant assure of it. Also, delayed process of investigation could result into re-formation of constituent compounds ultimately leading to unexpected result for your study.