Welcome, you've joined some of the finest quilters in the world. Anything that you need help with can be found here. I'm not being facetious, if there is a problem there is a quilter on this board that can help you. First of all congratulations on starting the quilt, my first one was just scraps and I muddled my way through it. I agree with the majority on removing the stitching you have already done. Do use a walking foot, it will make a huge difference. SID is the way to go in the beginning, but do begin in the middle and work your way out. Your little one will find so much love in her quilt that there is no way she will ever be chilly. Oh, a seam ripper is without a doubt the best tool a quilter can have in her arsenal. Please post a picture of your finished quilt, it is going to be gorgeous for sure.

If your quilt has shifted that dramatically, I would definitely rip the stitches out (I know that can be painful after all that work), then purchase a walking foot if you do not already have one. I could not have quilted all the larger quilts I've made without one, it will make it so much easier all the way around. I have done twin size quilts with just squares, then I used a semi-short zig-zag stitch starting at one corner, then moving over to the next square and do the same until you need to switch the quilt to stitch in the other direction; which makes it so much easier.

I've been machine quilting for about 20 years.
Did you make your backing and batting about 4" larger than the top? I use curved safety pins for machine quilting, a walking or darning foot for quilting.
I lay my backing(wrong side up) out on 2 large tables and tape it to the table, so that its taut but not stretched with no bubbles. Center the backing and batting on the table and the quilt top too.
Next I lay the batting on top of the backing, smooth it out and then put the quilt top on that. Then I pin about every 4" all over the whole thing.
Sharon in Texas

Attitude is important at this time. Put on some relaxing music.

Seam rip in short bursts. Try to enjoy this activity as well.

Yes, the walking foot is what you need. Also, when using the walking foot, slow your speed to about half speed on a Brother machine. I did not know this and it cost me a second walking foot to learn it. We learn from each other's mistakes all the time. Walking feet cost about $15 or so, but so very worth it.

Don't worry every quilt is full of ripping out sewing. Everyone has given great info. Begin in the middle and. Work outwards worked for me with a longer stitch than normal and a walking foot are essential.
Quilting is practise, practise , practise and practise oh did I mention practise. It is the hardest part for many to get.

I had exactly the same problem with the first quilt I attempted to quilt. Bought a walking foot - problem solved. Love my walking foot.