I’m sorry OP, but it’s not quite.
Aelius was the surname of a prominent family in Ancient Rome and the female form would have been Aelia. The original meaning is not known. One theory is that it may have been a latinisation of the Greek word ‘Helios‘, which does mean ‘sun’.
Naming a girl in 2022 Aelia with the intended meaning of ‘sun’ is a bit of a stretch. Is the meaning or the Latin important? How about Aurora, Roman goddess of the dawn?