Hi there, welcome to rabbits united!
You have to be very careful introducing a new bun to your bun, you can't just put them together, they will fight, they can be territorial little things! Especially the females! Do some googling on bonding rabbits, there is lots of info out there on how to get two rabbits to be friends, it can be tricky at times, I'm trying to bond two buns at the moment, but it is well worth it.
As to your existing cage, it depends what size it is. Most pairs will need a 6 foot long large cage, or a large two tier one, but if its big enough there is no reason why they can't share it once properly bonded.
As to age, your bun is a wipper snapper really so another young bun would be fine.
Have you considered adopting a bun from a rescue? RSPCA etc? They will usually let you take your bun along for bunny dating where your bun can meet the others and see who she gets on with, it is usually a good way to start as if your bun likes the other bun chances are the bonding will go well.
And finally it is so heartwarming to read that you want to get a friend for your bun, you will improve her happiness by 1000%, there is nothing nicer than seeing two bunnies playing, sleeping and cuddling together, you are doing the right thing by getting her a friend of her own kind.
Good luck. And feel free to post any questions on this forum, there is so much knowledge and experience here, I know, I'm making use of it too!