That's funny about you wanting to take her with you to work. I went through the same thing, so I actually did take my son to work one day, at about 3 months. I worked as a Java programmer at the time - and my boss was absentee, so I was just like, I'll bring him with me. It was totally distracting for me and everyone else. : ) It was a big room with lots of cubicles. Babies make more noise than you'd think. So, in the end, I was like, What was I thinking? Doh! It's a great idea ... in theory!
Good to focus on the positives, like the hot coffee and Christmas presents. Plus, knowing that he was out and about in his pram or napping or getting a bath while I was at work helped a lot. Sometimes, I don't know, I kind of wanted to share with someone else what a sensational child I had! More reasons to talk about his cuteness! In retrospect, I must have been awful.
So, yes, totally natural to want the child with you at all times. A great thing, in fact. Not terribly feasible, as I found out! And, I am glad I work, because I can provide more, like fancy camps and music lessons. And, it is is a good role model for the child, too.
Enjoy your time with her! You sound like a great mom!