I agree with all of the previous posts.

1. Your backing wasn't stretched taut to begin with and starching it will help control puckers and slide through the machine easier.
2. Spray baste or use pins to tack more closely than you did.
3. Loosen the pressure on your presser foot.
4. Increase your stitch length. Quilting is quite a bit bigger stitches than sewing
5. Practice on a scrap before loading the real deal but preferably a scrap made of the same stuff as the real deal.

Like CKCOWL said, the walking foot is not a magic cure-all. It can only work like it is designed to, on a properly prepared base.
I have one, but am not impressed with it. I can do just as well with regular foot.
You might find your foot pressure is too heavy for the thickness of a quilt sandwich.
Longer stitches tend to look neater, too.
Check your bobbin, again. Sounds like the bobbin tension is not correct.

I agree, starching heavy on the back would help

I agree...Please re do your quilt sandwich and use any brand of quilt basting spray..Remember to do a sample first...Also use a walking foot...

Along with the other issues mentioned here, I notice that your quilting stitches are running the same direction as your basting stitches.

Be sure to baste thoroughly and in both directions, side-to-side, and use a walking foot to avoid having your quilting stitch "push" the layer of fabric forward.

Jan in VA

I appreciate all the advice. I will definitely rebaste and try again. I used two boards when I basted it so it would be tight. I'll try to tape it down this time and also use the basting spray.
I have a couple of questions. How can I set the pressure on the walking foot? Is the "tension" the same as the "pressure" on the foot? I have the tension set at "1". I have a dial that controls tension, but I don't see any other setting for pressure. Also, how would I control the bobbin tension? My machine is a Brother with a Disney emblem. It has a drop in bobbin with a case that doesn't normally come out. I take the bobbin case out when I clean the lint out. Does the little screw on the bobbin case affect the bobbin tension?
I hope these questions don't sound too dumb. I have gotten some great advice and I appreciate it so much.

When I took a quilting class, we took a sample sandwich and drew lines across it at 1" intervals marking each with a number starting with 1. Then we set the tension to 1 and sewed from the first line across to the second line. There, we changed the tension to 2 and sewed from line 2 to line 3. And so on. At the end, we took the sample out and looked at the front and the back to see which tension worked best.

As for your problem: I think too that the backing is not taut enough and therefore, the sandwich is too loose. You may want to use the walking foot and make the stitch length longer. At least 3 or 3.5mm.

I agree with everything here. Wondering if you taped your backing down when you sandwiched everything so that the backing was tight before you started. It looks like you have too much fabric. If you don't want to take it apart, you might be able to just tie it and check it up to experience. It's difficult to tell by just looking at the picture.

I have to make the backing tight, not taunt, TIGHT! when I machine quilt. I have it almost like a drum when I baste it and I never have puckers or wrinkles. My big quilts, I have a LA baste them for me and I get too much fullness because the backing isn't basted tight enough. I have to smooth the backing out as I machine quilt it. I have never gotten it too tight to distort, it's all I can do to get it tight enough.

The dial with numbers on it is your thread tension and should probably be set at 3 or 4 but it varies with the type of thread you're using.

Presser foot pressure is a knob on top of your machine--usually above the presser foot & takeup lever area. Not all machines have a knob to adjust the pressure. Those that don't have to be adjusted manually which is more than you want to try.

Bobbin thread tension is set with the tiny screw on the bobbin case. Tiny little turns make big differences so you may want to mark what it is factory set it now with a marker or fingernail polish before you change it.

My advice for now is to make a small practice sandwich, preferably with the same materials as the real quilt. Change your upper thread tension to 3 and lengthen your stitch length. Spray, pin and/or thread baste your practice sandwich--don't forget to starch the backing first & tape it down taut--and then just play with the upper thread tension & stitch length until you're happy with it. You might also want to try without the walking foot. It's possible that your walking foot is applying too much pressure to the sandwich especially if you don't have an adjustment knob.