Carers Allowance & private pension

Just want to double check something.

My Mum gets Carer's Allowance for me. She is due to turn 60 soon and will receive a small private NHS pension from when she was a nurse for 8 years.

The NHS pension is approx. £300 a month.

As I understand it £300 a month is less than £139 a week which is the earnings cut-off point for Carer's Allowance; so she will still get her Carer's Allowance.

Edit to add: she doesn't work or receive any other income or benefits.

Is this correct?

Thank you.