Quilting over the applique on the back will be just fine.

Here is an idea. After you sandwich the quilt mark out the area where the owl is on the top of the quilt with light tack masking tape so you know where it is when you quilt. do the whole quilt with the meandering except for the taped area. After you are done do some hand quilting around the owl to outline it. The front of the quilt will have the image of the owl. Like getting two for one! I hope you can understand my explaination of this concept. Have fun quilting and post when done!
peace :thumbup:

EDIT: After looking at this cute quilt again I think this idea may not work because the owl may overlap some of the applique on the top of the quilt. Just a thought.

It will look fine!

I had hoped to do something like you suggested but the owl is right where the flowers are on the front. So, part of the owl would be quilted and part not. Still undecided as to what to do. Maybe two quilts is a good idea. Thank you all for your input. I will have to decide soon - this quilt(s) needs to be finished this weekend.