What was Queen Elizabeth's nickname as a child and what type of dog did she like? 

When Elizabeth Alexandra Mary, the elder daughter of Prince Albert, Duke of York, and his wife, Lady Elizabeth Bowes-Lyon, was born on April 21, 1926, she apparently had little chance of assuming the throne, as her father was a younger son of King George V.
But in late 1936, her uncle, King Edward VIII, abdicated to marry an American divorcée, Wallis Simpson. As a result, her father became King George VI, and 10-year-old “Lilibet” (as she was known within the family) became the heir presumptive to the throne.
Though she spent much of her childhood with nannies, Princess Elizabeth was influenced greatly by her mother, who instilled in her a devout Christian faith as well as a keen understanding of the demands of royal life. Her grandmother, Queen Mary, consort of King George V, also instructed Elizabeth and her younger sister Margaret in the finer points of royal etiquette.
Educated by private tutors, with an emphasis on British history and law, the princess also studied music and learned to speak fluent French. She trained as a Girl Guide (the British equivalent of the Girl Scouts) and developed a lifelong passion for horses.
As queen, she kept many thoroughbred racehorses and frequently attended racing and breeding events. Elizabeth’s famous attachment to Pembroke Welsh corgis also began in childhood, and she owned more than 30 corgis over the course of her reign.
Queen Elizabeth's nickname was Lilibet, and she liked Pembroke Welsh corgis. 