Those "big stitches" are probably her basting stitches.
You have some great suggestions here, tiger tape among them. Since you mentioned you wanted to use what you have on hand, perhaps you could use our sewing machine's regular stitch length as one would he tape. Just stitch a long row, or even several long rows all with the stitch set at different lengths, and practice making your hand quilting stitch beside them, or beside every other one.
More tedious but perhaps as effective, use a very sharp graphite pencil and a ruler to mark a dotted line every 1/4 inch or 1/8 inch, or mark in centimeters if the length is better for you.
Use these to practice handquilting on a block or circle or oval and use a colored thread. When you have quilted the whole design, make a small pillow from the work and then go on to your quilt.