First, Welcome to the QB and the world of quilting. You've joined a large group of quilt lovers and we all like to see your quilts and give as much encouragement as we can.
Your grandmother's flower garden is certainly lovely. And they are a lot of work. I know because I've made one. It looks like the fabrics in your quilt are from the 1930s-40s. It could be as early as 20's but that flowery yellow fabric looks very 40's to me. Anyone can duplicate a past pattern like the one you have. What really tells the story about age is what fabrics are used. There are people out there that can tell you very closely the age of the fabrics. I'm not perfect at it but, since I've been sewing since I was 5 (63 years ago) and taught sewing most of my working life, I'm not too bad at it. There is just a look to the patterns (certain patterns were trendy at a specific time) and the weave (30's and 40's fabrics are not as tightly woven as today). But, doing a little research, visiting some museums, etc. will certainly help educate you.
Whatever the age, you certainly have a treasure. It would have been nice if our grandmas and aunts would have put labels on their quilts. But that just wasn't done back then. The quilts were made to use for the most part. And time was precious.... no need for extra work. I'm so glad that putting a label on has become popular. Our children need to be able to know about our work. Hopefully our quilts will last a long time.
I hope my comments have helped you...... quilt on!!