Ridgerunner has it right and there is little that I can add except to remind you about the following.
There are several reasons that a hen or pullet lays soft shelled eggs. Old age, a calcium deficiency, diseases of the reproductive track, and yes the very young, and a 4 1/2 months old is very young for a pullet to start laying. However the most common reasons is a deficiency of vitamin B3. A hen requires a good source of B3 to be able to convert dietary calcium (crushed limestone rock, spent egg shells, or ground up oyster shell) into bone tissue. Every egg shell comes right out of the hens' skeleton and what we feed them in the way of oyster shell etc. is first used to replenish or reinforce her skeletal system.
All three sources of calcium, egg shell, crushed limestone, and oyster shell are a goon source of dietary calcium. However spent eggshells are so small, fragile and light in nature that they can't remain in the digestive track long enough for the hen's digestive track to absorb the calcium in eggshells. Animal protein is about the only source of vitamin D3. Fish especially cod liver oil is the most important or richest source of vitamin D3. Beef liver (preferably raw) is another good source. Vitamin D3 is a necessary vitamin required for a hen to utilize calcium. Without D3 she just leaves your calcium on the poop board.
Would adding a bit of cod liver oil to the feed on a regular basis be a good idea? Or just feed a decent amount of raw liver?