She reeeeeally doesn't need friends right now. You do. But she doesn't.
She needs warmth, love, and security. Which is learned from getting her needs met (food when she's hungry, comfort and closeness of touch and being held, changed when she's wet, rocked, and loved, and talked to, etc.)
Other babies and small children/toddlers are completely incapable of meeting these needs (in fact, usually, they're counterproductive)...They're interesting... but so is a glass mason jar filled with water... so is singing... so is licking the couch. Those things also don't scream in her ears, pass diseases, pull her hair, pinch, scrape, gouge eyeballs, hit, kick, bruise each other up, knock each other over, and in other ways cause physical and emotional pain (ask any mum with twins or siblings)... all the things that infants and toddlers do to each other. She isn't capable of making friends right now. She IS capable of forming bonds with people... but those take hours and hours and hours over days and weeks and months. Even then... she'll still pitch a fit and want nothing to do with mommy or daddy or nana for awhile and only want ONE of them. (Those are hard phases whether you're the person needed or the person rejected).
You sound like a very caring mum. So keep those ideas in the wings for a couple years. Even at 2-3yo she'll mostly be doing "parallel play" and "copying".
Our kiddo's an only as well. And he's SUPER social. So don't sweat it just yet. Just love on her and provide that foundation of trust that friendships can be built upon later. Like Denise P... we're busier than a one legged man in a bum kicking contest. I have to look weeks ahead for playdates. Kiddo (7 going ong 8)has 6 really really good friends. And these were all made in the past 18mo (after moving). Which is another thing to keep in mind. Unless you're from a very very small town... she won't go to the same preschool with probably any of the babies you know or toddlers you'll meet later. And then they'll split up again when it's time for school. Not to mention people moving. So it's not like sibs... where she's going to be with them for years and years. People will be coming and going out of her life. There is no instant sibling option. So now is the time to form a rock solid foundation of love and trust with the people who WILL be in her life. You, your partner, grandparents, etc. People who will love her unconditionally so that she can weather the hitting, kicking, biting, and "I'm not your friend anymore!!!!"s in her future.