I can't imagine staying home without young children. I can imagine staying at home with young children, but have never had any desire to do so. But every person is different and ultimately, people should do what's right for them.
One of my proudest moments as a mother was when my daughter, when she was 8 or 9, told me "I'm proud that you work, mommy, it makes me feel good." I'm sure she would have also been proud of me if I stayed at home, but because it's what she knew, she was proud that I had a good career (and she still is).
When our kids were finally both in school (Grade 5 in our case), my husband and I sat down and looked at the pros and cons of having me reenter the work force. And when we looked at the impact it would have on the lifestyle we'd come to enjoy, we decided it simply wasn't worth it. We enjoy the way we live too much to want to change it. Especially as we didn't have a pressing financial need for the extra money I'd bring in.
My husband likes coming home to a hot dinner, and I enjoy making it for us. He likes the fact that I can run errands and do housework and home maintenance during the day, leaving our evenings and weekends free to spend together doing things we enjoy. And so do I. I very much enjoy having the freedom to set my own schedule, choose my own tasks, and not have to answer to anyone except myself. I'm always working on different projects.
Its lovely when our children say they're proud of us. Mine have told me they're proud of me, too, though I've never had a career of any sort. They're proud of me for writing a book, for building websites, for knitting blankets for their beds, for teaching them and other kids to read and do sums, for being home with them, for making cupcakes or bread or soup when they were sad or stressed, and for all sorts of other things that I'm sure most parents do, working outside the home, or within it.
Your career is a point of pride for you, and your daughter's support is important to you. I have other things that are important to me, and I appreciate my children's support, as well.
My mother worked throughout my childhood, even earning her doctorate while I was a teenager. I was (and am!) proud of her, too, even if I didn't choose to follow in her footsteps.
The only thing that stings, is that my mother has made it sadly clear on several occasions that she's disappointed in me. She envisioned me having a career and she feels like a failure as a mother because I didn't pursue one, even though she tried to be a good example to me. So please, if your daughter ends up without a career of her own, don't be disappointed in her, or make her feel in any way that she's wasting her talents.