If feasible, I would do all 3 time points you suggested. If you use alamar blue, you can take reading and place the cells back in the incubator. Doxorubicin should bind DNA rapidly, but cells may need to cycle to reveal the cytotoxicity.
This is common question when determining IC50 values from in vitro proliferation assays such as MTT and MTS. You will get different IC50 values depending on the time point you use, especially if you are leaving the drug on the cells the entire time. If you have no previous data to work off, it is a good idea to try each of those time points, and then report the IC50 values specific for each time point. However, keep in mind that when making comparisons between different cell lines, or to previously published work, you would need to keep the time point consistent (along with all the other parameters of the experiment). You may find that some drugs have no effect after 24 hrs, and so longer time points are necessary. This is also true for cell lines that grow very slowly, where longer timepoints may be needed to see a difference even at high drug concentrations. In my experience, 24 to 48 hrs of Doxorubicin treatment produces a good response curve with most cell lines. I have also noticed that for some cell lines treated with Dox, the IC50 values calculated after 24hrs will equal the IC95 values after 72hrs of treatment. Hope this helps.
I agree with Adam Karpf and would also do all the time lines. However, please keep in mind the reason of calculating an IC50, because it may influence your time-point selection. Why are you trying to kill (or inhibit the growth of) half of your cells? If your future experiments will rely on this data, maybe you only need a dose which kills half of your cells at a specific rate (like 24 hours). One of the common misconceptions about IC50 is that people treat it as if it is a general property. It is not. IC50 results heavily depend on your specific conditions (number of cells you have seeded, the amount of serum you have used etc). Therefore, you should determine it for yourself and your experiments (and choose the incubation period accordingly).