Hi, Ash and sennie! You did not tell us her name -not that it makes any difference for the reply to the question, it's only that we like to know because we are nosy and love all birds
A baby bird does not have a full molt until it's second year of life. The first molt is called the 'juvenile molt' and it's not a full one, it's a partial one because they only molt contour feathers [rarely down and never any primary, secondary or therciary feathers]. As to when it's supposed to happen... well, that depends on when it was born [whether on or off season], what it was fed [soy or no soy] and whether it was kept at a strict solar schedule or not.
Now, at almost five months of age, that means she must have been born in May so, although they are actually more short day than long day breeders, May is not that bad IF the birds are not being bred all year round [which breeders tend to do]. I assume that the breeder fed it a soy-based formula and that you have been weaning it with soft foods that don't contain any soy as well as keeping it to a strict solar schedule with full exposure to dawn and dusk so, if this is the case, she could be having her juvenile molt around now. My senegals are all done with the molt but they are adults, they have been kept at a super strict solar schedule and have not had any soy for many years so they are perfectly in tune with the seasons - with babies, it's never that accurate because of breeders bad practices. But, in any case, loosing a lot of down or looking ratty is not a normal thing so do review your husbandry [diet and light schedule, primarily] and keep an eye on her, just in case.