Sorry you're going through this, OP. That sounds incredibly stressful, frustrating and unfair.
The Renters Rights Act was supposed to protect against discrimination towards people with children or in receipt of benefits, but landlords can (understandably) still carry out affordability checks, so in practice those provisions are likely to have limited impact for many people.
Given your circumstances, I would contact the council's homelessness team, and now, rather than waiting until the notice period is close to ending. Although see what I say towards the end about which council to approach. You will be classed as threatened with homelessness once you are within 56 days of the section 8 notice ending. At that point the council will owe you a prevention duty, which means taking reasonable steps to help you keep your accommodation or secure alternative accommodation that is suitable for your household and affordable for you. However, there is nothing to stop them helping you sooner and they are supposed to do so to avoid a crisis, especially if there is no chance you can stay longer and you have a disabled child.
If homelessness cannot be prevented, the council will owe you a relief duty (to secure you accommodation) once you become homeless because you will be classed as being in priority need due to having a child. Typically, this will be temporary accommodation until they can find you something settled. As others have said, the council may tell you not to leave your current house until the landlord has obtained a possession order and warrant. Councils often do this because temporary accommodation is in short supply and sub-optimal, so remaining where you are is usually preferable. However, they must only do that if they consider it to be reasonable for you to remain. If the landlord genuinely intends to sell and is likely to pursue possession, there may come a point where remaining is no longer a reasonable option. They should also take into account that there can be negative consequences for you if you don't leave - bad reference from the landlord, possible court costs etc.
As you might need to access temporary accommodation, I would make sure you have clear evidence of your child's needs. Certain types of temporary accommodation might not be appropriate and if you can get your GP and any other professionals involved to write a letter about suitability that would be helpful.
I would also make sure you are registered for social housing immediately if you are not already. There is no guarantee of a social housing allocation, but it is a route the council should be considering given your circumstances and the affordability issues you are facing in the private rented sector. Having a disabled child should give you some priority. Being homeless definitely will.
In terms of finances, if you are on UC I would expect you to be entitled to the housing element. What you receive depends on the local housing allowance (LHA) rate for the area. If the LHA rate is insufficient to access private rented accommodation locally (which I assume is your dilemma), that will push the council towards a social housing offer. That said, it is also open to councils to top up your income if nothing is available that is suitable and affordable within the LHA rates. Lots of councils do this so definitely ask about it. Having a disabled child will mean they need to consider this anyway, unless there is a good supply of decent temporary accommodation hat is suitable; most unlikely!
You mention your parents live in Dorset. If relocating closer to be near them is something you would genuinely like to do, don't rule it out on affordability grounds. The LHA rates for Dorset will be different to where you are. You can apply to go on the housing register there if you parents have been continuously resident there for at least 5 years: https://www.dorsetcouncil.gov.uk/w/housing-register-eligibility-criteria. Under the Equality Act councils also need to consider needs arising from your child's disability, including if you need to be close to family for support.
If you do apply for homelessness assistance, think carefully about which council to apply to. You need to have a local connection for the council to owe you various duties. It is not only through your own residency that you might have a local connection. You will also have a local connection to a district where close relatives have lived for at least 5 continuous years. So, if you do want to move to Dorset and your parents meet the 5 continuous years test, you could apply there. I would get urgent advice from your local CAB or Shelter before making a homelessness application if you might want to go to Dorset. There is nothing to stop you joining both your local and the Dorset housing register now though.
Hope this helps.