Entitlement to Income Support as a Carer is dependent on you being in receipt of Carer's Allowance. Your father's award of low rate AA would be sufficient for you to claim Carer's Allowance and subsequently Income Support, but you would have to at least have the claim for Carer's Allowance in before you can claim Income Support.
One word of warning - if your father currently lives alone or with someone who is also disabled, and is in receipt of means tested benefits (Pension Credit) the amount of benefit he receives may be affected by anyone claiming Carer's Allowance for him. If he receives a 'Severe Disability Premium' on his Pension Credit, he may not want you to claim Carers, so just check this first.
Hope this helps!