You may come before your daughter through age. Even though your daughter is vulnerably.
You can get the vaccine along with your daughter. When she is called make sure you are included. Are you registered as her carer at her G.P. Regardless of you being mother and daughter. If your daughter is an adult and can make decisions. Your daughter has to give consent to be her named carers as her G.P.extremely vulnerable list
Likewise if you are called first though age. State the reverse as get vaccinated together.
You can also register at your G.,P. as being a carer.
As you are claiming carers allowance there should be no problem.
Make sure if challenged you have a copy of your carers allowance.
Hopefully it should not be necessary.
Some unpaid carers have a carers id card. As they are registered/member to a carers organisation in their area.
I have a unpaid carers photo ID.
https://www.gov.uk/government/publicati ... ember-2020