As to her 'hair' well it is typical of Gloster canaries, although Glosters aren't usually this yellow they are usually more green like her head colouring but all over, and they aren't usually as fluffy as Tilley is.
My guess is one of her parents might have been a Roller Canary as they are more 'ball' shaped and a bit more fluffy.
I think her 'fringe' could do with a trim though as she tends to rub her head on the bars or perch to shove the feathers up to be able to see better, so I expect Tilley would call this 'hair cut' a bit of a disadvantage.
My personal favorites are rollers, amazing singers. The males sing best. Listen in the shop whistle a bit and if ther is a singer there he is likely to let rip. Sounds so good makes your heart sing too.