by 1.5ml subcutaneous injections, i assume you're referring to either estradiol valerate or enanthate at a concentration of either 40 or 50mg/mL? if so, you're doing monotherapy - that is a high enough dose that it'll almost certainly be enough to suppress your body's testosterone production, and even if the exact dosage may need to be tuned a bit (depending on what your blood work results say) that high of a dose is clearly intended to work without requiring an antiandrogen.

dutasteride may not be a proper antiandrogen, but blocking DHT (dihydrotestosterone) can be useful for combatting the effects of male pattern baldness. now, since estrogen monotherapy will lower your ordinary testosterone levels by approximately an order of magnitude, your DHT levels should drop by about the same amount (since DHT is primarily produced via conversion from ordinary testosterone). this should be more than enough to avoid going bald since ideally your DHT levels will end up at about the same level as a cis woman (and may even be enough to revert some hair loss - i have two little patches of baby hairs on either side of my widow's peak which started showing up around february!), but if you've already lost a decent amount of hair then taking a DHT blocker could be helpful on top of that to increase the likelihood of some hair growing back.