http://www.royalcollection.org.uk/egallery/object.asp?category=AAPICTURES&object=405741&row=309
If you magnify the image, I believe the girl to the right of Augusta & the baby is Princess Elizabeth. Elizabeth & Louisa were the invalids of the family, according to a web source I have forgotten, & perhaps Elizabeth was generally not strong enough to sit for a portrait... I don't know.
I just looked Elizabeth and Louisa up in van der Kiste's book. Elizabeth's health was so bad that she had not been taught to read by the age of eight. She was artistic though, and loved taking part in theatrical performances. Sadly she couldn't stand upright unaided but learned her parts in plays simply by hearin her siblings rehearse them. It was inflammation of the bowels that killed her.
Louisa was at first chosen to follow in the footsteps of her namesake aunt and become Queen of Denmark, but the Danish envoy thought she didn't look long for this world so chose Caroline Matilda instead. Since their sister Augusta's marriage the two had become much closer, and Caroline Matilda was very sad to leave the tubercular Louisa, probably knowing they would never meet again.
Some interesting things about other family members too - Anne, the Princess of Orange, was always on the look out for husbands for her sisters Amelia and Caroline, whether they wanted them or not, so much so that Amelia wrote to her: 'I sometimes believe you think that unmarried women have no places in heaven, for you think nobody can have the least happiness without being tied from morning to night to a creature which may tire one's life out.' Anne was clever and hardworking, but had no charm whatsoever - she died of dropsy. Their sister Mary, Landgravine of Hesse, was abandoned by her husband, who wrote to her saying that before their marriage he had been in love with a well born Catholic lady who wouldn't marry him because of his faith. However, on her death bed this lady begged him to convert so their 'souls might be together in heaven'. This he did, of course. George II was furious and ordered Mary to come back to England, but she refused, saying 'it was her duty to remain in the situation in which it had pleased God to place her'.
Amelia, of course, remained a spinster, though she acted as hostess to her brother the Duke of Cumberland, and they were often invited to parties together. She was the only one of George II's family with him when she died, though she was ill herself and almost deaf and blind.
Augusta, eldest sister of George III, was very bold, quick witted and argumentative, though apparently had a tendency to over eat, and paid no attention to her mother's pleas to be careful about her figure.