It's a very cute bunny! Yes, rabbits do need to be spayed, although as young as your bunny is it is still possible that it's a male. Missexing is common in younger rabbits, especially from sources like markets.
Generally, the best choice for a companion for a spayed female is a neutered male, although each bun has their own personality, of course! Your best bet is to have your rabbit spayed, wait for her to heal and for her hormones to settle down, and then visit a local rabbit rescue to do some bunny "dating" to see which rabbit your rabbits likes.
I'd recommend reading rabbit.org for care information on rabbits since you're a newbie. Make sure your bunny has unlimited hay!
We are as gods to the beasts of the fields. We order the time o' their birth and the time o' their death. Between times, we ha' a duty. - Terry Pratchett.
"Men have forgotten this truth", said the fox, "But you must not forget it. You become responsible, forever, for what you have tamed. - Antoine de Saint-Exupéry