Most ovarian cysts resolve on their own within a few cycles / months, no intervention needed. According to this doctor-authored website - http://ovaryresearch.com/ovarian_cysts.htm - hemorrhagic cysts always resolve on their own. The cyst isn't that big either. The 1.5cm one is "tiny" and it's not uncommon for cysts that appear to be complex to end up not being so (such as your other one that is "likely hemorrhagic").
I don't know why your doctor would be recommending surgical intervention especially at this point. But also concerning is that she would remove your ovary instead of JUST the cyst (cystectomy). As Dr. Parker says on the aforementioned webpage, one should almost never need to lose their ovary for an ovarian cyst. Removal of any part of the "reproductive" system (one ovary, the uterus, tube or tubes) can disrupt normal ovarian function. And our ovaries are essential our whole lives for hormone / endocrine production. Removal of both ovaries or their impaired function is associated with accelerated aging and increased risk for many health problems.
Another ultrasound in 6 weeks or so would be more appropriate.
My organs were unnecessarily removed for a 9.5cm benign ovarian cyst when all that should have been removed was the cyst itself. The many lifelong functions of the ovaries and uterus became apparent very quickly. I discovered some very disturbing facts about the hysterectomy industry (and my gyn's unethical tactics) through my medical records and research. I discovered that women's organs are removed unnecessarily approximately 90% of the time.
Please keep us posted.