Yes.I’ve done this before for a friend in Thailand coming to visit. They had to do the same form and application fee all over again for each of their two children.The children didn’t need to be fingerprinted though. Although they did take them to the visa application centre with them (it was the school holidays at the time), I don’t remember if the children were actually required to be there (sorry).If you’re travelling in term time, they will ask for a letter from the child’s school giving permission for the trip (but this is probably not an issue for a four year old).