I have to give kudos to the last two responses - excellent advice!
I understand it is SO hard to stop nursing at night due to tiredness and emotional reasons, but it sounds like you're ready for a good night's sleep! Leigh R gave great advice about *gently* showing your baby that it's okay to sleep in his own bed. Just like we teach our kids to talk, use a spoon, use the potty, etc., we also have to teach them how to sleep independently.
Just prepare yourself - it WILL be heart-wrenching, especially if he can cry 'mama'! Remember, he knows no other way of sleeping and this is a teaching activity. If at all possible, take a solid 3 nights to do this tactic, being consistent night after night, and by all means DON'T give in. You may even want to arrange for someone (family or sitter) to come over and help you during the day so that you can take a nap to prepare for the night's disruption. It may not take that long, but if you expect to solve it in one or two return trips to his bedroom then it can be easy to think it's too hard and give in or to think you're damaging his little psyche. The other comment about having your husband do the 'night training' would be great if at all possible. Even at 13 months, kids are incredibly persistant and if you give in and bring him back to your bed it may be a very long time until you can break the habit. Just think of this as a very hard few days to ensure years of good sleep for you and your child. All things in parenting are hard work at first :D
My oldest daughter (now 3) was always a great sleeper and has needed lots of sleep, even today. My second (almost 2) didn't need as much sleep and she went through an I-don't-need-a-nap phase at about that age. With my girls being 16 months apart and a military spouse overseas ALONE while my husband was deployed, this mama needed a break! I enforced 'quiet time' for both my girls, regardless of if they actually sleep. I kept my oldest in her crib until age 3 by insisting that climbing out was not acceptable and she had to wait for me to come get her. I provided them with board books and a few safe toys on their nearby changing table so if they woke early they could have something to do. Oftentimes, they would wake to play and then go back to sleep. I sacrificed my own sleep and relaxation time to be strong-willed about this - after they both realized that just because they were awake (day or night) that did not mean it was party time! Of course, this was after they were both finished nursing in the night or every two hours. It did take a lot of practice and reminding and the 'no encouragement' tactic does work - just go in and lay them back down without eye contact or holding, just say 'it's time for sleep'....over and over and over! Like I mentioned earlier, you have to teach children good sleep habits just like any other skill. My oldest enjoys her quiet time, especially now that she's in a big girl bed. She has a basket with Barbies and paper-paged books and a few other special 'big girl' toys that her little sister is too small to play with. Sometimes she doesn't take her nap, but she at least gets some time for rest and I get a time for rest.
It's not easy and it will cause some stress for you - but so will having a toddler in your bed. Some people don't mind having a 2+ year old in their bed and that's great for them, but I certainly can't and it sounds like you are ready for the change. I would highly recommend the Baby Whisperer by Tracy Hogg. That particular book is geared toward helping newborns sleep in their own beds, but she does speak to how to re-train an older baby. There's also a Toddler Whisperer - I haven't read it but I've heard it's the same principles but for toddlers. There's no way I'd have been able to handle my two kiddos so close together without that book!
Good luck!