From a quick Google, puberty in bulls happens around 11 months of age. Shetlands do mature quickly but I would doubt whether Hagrid, at 14 weeks, is the daddy. He was awful wee to be away from his mammy?
We had a bull work successfully a week short of his first birthday but I can't see a three month old calf being ALLOWED by the senior bull to get anywhere near an ovulating cow, and while lust finds a way, I can't see that Hagrid could reach. Fourteen weeks is just a baby.
Colour genetics is complicated and I am far from being an expert. Ruth Dalton is the most knowleageable person I know on colour genetics in Shetlands. As far as I understand, red is recessive so both parents must carry the gene and the calf must get red form each aren"t - if she's had 8 calves, there's a 25% chance of a red calf, simply by chance. She's just bucked the odds, if the calf is Beano's.
If you have doubts about the parentage, you shoudl have a DNA test done before registering the calf.