Disclaimer: I'm not muscling in on JK's turf - just gambolling on it, like a spring lamb, having fun working out the literary and psychological puzzles which she is having fun setting us.
"Oh for pity's sake - not another monster? You really cannot keep bringing these things into the school. Surely you realize that?"
"But I hatched the egg meself, an' she won' do no harm, I know she won' - look, she's only little, see, not much longer 'n me thumb. An' pretty!"
"I know you think that every be-tentacled monstrosity you meet is really just a great big softie that's been misunderstood... but sooner or later one of your little pets is going to kill somebody. I mean honestly - a basilisk! Really, you've gone too far this time, Salazar."
According to Fantastic Beasts and Where to Find Them, it was considered remarkable for Herpo the Foul's basilisk to have lived "close on nine hundred years", and the males have a scarlet crest. There's no mention of Slytherin's basilisk having a crest, and it was in his possession about a thousand years ago - so it's a female, and must have been very young when he had her.