Her death record doesn't appear on 'deceased online'
The simplest way to find her exact date of death is to order a copy of her death certificate - it costs £9.25 and usually takes about a week.
Order here: https://www.gov.uk/order-copy-birth-death-marriage-certifica...
Quote registration district Dover, date of registration December 1987, volume no. 16, page no. 1206, reg no. 1287.
Details from her death certificate may well give clues as to her place of burial/cremation. Good luck!