I'm at the "other side" of the difficult bit with a new DC2 and couldn't read and not post. My DC2 is now 20mo.
This too shall pass...before you know it your DC2 will be sitting up and crawling and interacting with your DC1 and you will have given both DCs the best gift in the world - each other. My two play together now and DC2 gets upset when DC1 goes to school, he misses her!
In the meantime, a sling is a great idea. How about some new toys or DVDs for your DC1 as a special treat, perhaps tell her they are a present from the baby to say sorry for taking so much of Mummy's time at the moment? Put out the toys or get a book ready to read together when you sit down to feed. How about a baby dolly of her own?
When you are feeling a bit more up to it, put the baby in the pram at nap time and head to the park with DC1.
Don't be afraid to pull her out of nursery for the odd half day to spend some time together. Or can she go in late or leave early? The money is paid regardless!
I'm going to be controversial and suggest introducing a bottle a day so that DC2 is not so reliant on you being there for feeds. I didn't do this with DC1 but did with DC2 and it did mean that DC1 and I could "escape" every now and again for a bit of us-time, knowing he would take bottles. I have fond memories of a morning when DC2 was only a couple of months old and I relinquished him to MIL for a day (she loved it) and DC1 and I had a day out, just us. I missed DC2 more than you can imagine, but DC1 needed me too.
DC1 and I regularly have girls' days/girls' time now DC2 is a bit older, I pop him into nursery for an extra day if she has a teacher-training day and we have a day out together.
You won't lose your bond with your DC1, your DC1 will have to learn to share you, and get to know daddy a bit better, but soon enough you will be out the other side of this, like us!
Good luck x