Welcome. I think you have a few issues here.
You're a beginner, and gloves are not a super easy beginner project.
You only have 10mm needles. Those are big needles using very thick yarn--not the easiest to start with.
So this is what I suggest. Make her a scarf. That's a great and easy first project. If your scarf turns out good, then you can make a hat to go with it. Pick out a free easy beginner scarf pattern and get the right size needles and yarn to make it. Here's one. This pattern calls for 5.5mm needles and appropriate yarn for that size.
Before you start the scarf, get some extra yarn and practice A) casting-on and B) knit and purl stitches. Look on youtube for a video on 2-needle casting on or "knitting on" casting on. It's easy to learn by yourself. Then watch a couple of videos on the knit and purl stitch. Practice for a couple of hours before you start your scarf.
I hope this helps.