What is the likelihood of getting an Unqualified Resignation with ADSO and having no family care plan?

As many others have answered, resignation is only for officers.
As an enlisted SM you need to review obligation/options in AR 135-91 and separation requirements in AR 600-200.
If you have had your pregnancy verified and have been given a profile, your commander should counsel you with your options.
Do consider the pros and cons of getting out and how that will impact your ability to provide for your child (housing, food, clothing, medical care, child care....these canbe expensive).

You're not an Officer so no worries about trying for UR. You're required by regulations to have a FCP as a single parent. If you don't have a FCP, or fail to create a FCP, you can be chaptered for that. You could request a Pregnancy Chapter.

You can't request an unqualified resignation. Resignation is for commissions and you don't have a commission. You CAN request a chapter 8 separation (separation for pregnancy). Chapter 8 separations are routinely processed unless there is something else that may affect your situation (under adverse action usually).

Enlisted with an ADSO won't have it interfere with a Chapter 8 request (officers have to request it be waived), however you will still have your Military Service Obligation (MSO) which would continue in the IRR until you reach your eight year obligation.

I assume your command has already given you a pregnancy counseling and you originally stated that you intended to remain on active duty (that is, unless this pregnancy is recent). You are allowed to change your mind, however the separation date will be determined by your command after discussing it with the medical side (however, it will be normally be NLT 30 days prior to the expected delivery date).

Now that the answer is out of the way, I would be remiss in not pointing out that DoD and the Services have made significant changes in pregnancy/family policies* in the last few years, but I understand your situation as a new single parent. I would still recommend that you explore all the options available to you first.

Additionally, if you separate while pregnant, you need to make sure you pay attention to health insurance coverage. If you've served on active duty over two years, then you're eligible for enrollment in VA health care. You also could be eligible to extend your military health care through six weeks post-delivery, but you'll have to talk with your provider regarding this.
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* https://armypubs.army.mil/epubs/DR_pubs/DR_a/ARN35255-ARMY_DIR_2022-06-000-WEB-1.pdf