Should I get my kitten a playmate?

I got a kitten a month ago and she is is wonderful! She was found with her litter abandoned in front of a house, so I don't have background on her parents. But, she is very well behaved and a very happy kitty. My housemate, however, got a puppy and my kitten is extremely afraid of the puppy even though the pup is interested in the kitty. Since the arrival of the puppy, my kitten has to stay in my room for most of the day, because the dog gets out a lot. I was wondering if I should get another kitten for my kitty so that she's not so lonely and secluded. Is that the best option? If so, should I get a male or female? And, what age? Thank you.

How old is your cat? How long have you had it?
   
How long as the puppy been in the house? How old is he? (I need to know ages, here.)
   
What kind of dog? How big: is he now / is he going to get?
   
If it's only a few weeks or so, then not enough time has passed for the cat to adjust to the concept of The Playful Puppy. Cats are creatures of habit & can take some time to warm up to another animal (or just decide what to do about it). Your cat doesn't HAVE to stay in your room, your cat just doesn't want to deal with the puppy. The puppy isn't dangerous, he's just playful. To him, the cat is a warm body to romp with. The cat was probably taught by her mother that dogs were object of suspicion at best & danger at worst. This training has to be overcome.
   
I recommend that before you adopt another cat, let things settle down between your cat & the puppy. Don't keep your cat in your room; in fact, it would be a good idea to make the cat spend a couple of hours a day out with the dog. Haul Fluffy out every evening for attention while the puppy is in the room; just keep the puppy from starting a romping session at these times. And if the cat encounters the puppy at odd time, good; this is Real Life, Other Animals Happen, & the cat has to get used to it.
   
Let the cat hide from time to time; the cat has to decide to take this particular bull by the horns & deal with it.
   
I suspect that after another month or two, relations will likely settle down. The two may even become friends. Possible outcomes: The cat will decide to be friendly, & they'll become pals; - - The cat will be polite & civil to the dog, but not seek out his company; - - The cat will hate the concept of the dog & will eventually hiss, swear & whap him in the face & tell him to get lost (much to the Friendly Puppy's shock); - - the cat will decide not to care & ignore the dog entirely. I really don't think the sustained fear can last a lifetime, eventually the cat will get tired of being scared (it's wearing) & move on past that to one of the positions above.
   
If it's not working out in a couple of months & you want the cat to have a friend (& some back-up):
   
Best advice for second cats:
   
A cat about her age, of about her energy level;
   
I'd recommend a male, as two girls in the house often have turf wars & strained relations (experience, here);
   
Make sure the cat is rated dog-friendly (go to a local private adoption group, they usually vet the cats for relations with children & dogs; Petfinder is a good source of adoption groups). Being dog-friendly, the new cat may actively like the dog & may talk your cat into being more reasonable about the entire Dog thing.