Possibly late, but just in case.
1/ If its a public skating session there will probably be many people on the ice. If you use Auto-Focus chances are it will be jumping around all over the place on wider shots trying to pick a focus point amongst confusion of moving subjects... On tight shots, focus likely to change between focus lock and shutter release. You may find it easier Go manual.
2/ you will probably be trying to zoom in on your child; moment you go to press the shutter, some-one will zoom accross your frame! If tracking tight, use sequence to get shots either side of such events.
3/ Little people always look better from low angles. Hard to get them off the ice. I have got many better pictures, if not so technically great, getting on the ice with my kids, and shooting from wast level, with a compact.
4/ Flash with compact on ice. High ISO off the ice, & think about white-balence. Lighting is often 'strange'. Rinks near me have high cielings and aluminium insulation in the rafters, so you get a lot of bounce reflection from above and below, but mixed lighting on the rink from flourescent and tungsten. (often in different areas! Couple of shots have rather eirie effects, with natural color where I have used fill-in flash on my kids, but green-cast over ice from flourescent lighting, then orange cast in the back-ground, off-ice where lit with tungsten!)
5/ Levels are also quite deceptive. The amount of reflected light off the ice and silver cieling can make it look brighter than it is. YET, the amount of white ice, doesn't fool the metering to 18-grey as much as I expected. EXIF for some of my recent pics of Daughter; I was shooting at ISO1600 with +1 EV for white balence; but I was struggling to get shutter speed over 1/50th to freeze foot-work, at wider apertures. Where I have shot on auto; camera has on sport mode, been trying to up the ISO and giving very noisy pics, or has been selecting slower shutters, and giving blur. You may find that going manual or aperture priority saves the camera getting too confuddled.
6/ You wont need a lot of lens reach. Rinks are anoyingly large enough that 60mm+ may be tempting to try and get in on the target from one end to the other, but them kids move quick! One lens and move your vantage to get close; and think 'wide'.
Lastly Your subjects are Kids. Means Chaos. Hard to plan pics in chaos. A lot will probably be down to serendipity. Work with it! Fighting it is route to a nervouse breakdown!