Welcome to Science Buddies! This is a really great chemistry project.
The 3% hydrogen peroxide will oxidize the iodide to iodine, but it might take longer or require a larger volume. I recommend doing a small pilot experiment using a known iodide solution if this is available. Try using 50% more hydrogen peroxide for this step.
The original directions specify using a 50 cm length of kelp, and I would guess this would be about 100 grams of fresh algae, or about 15 grams of dried algae. The ratio of fresh weight: dry weight for kelp is about 6.5. http://www.fao.org/docrep/field/003/AB724E/AB724E07.htm
Again, however, you are working on an original idea here, so the pilot experiment would be helpful to verify results before you proceed with the complete experiment.
I recommend using the quantities of reagents specified in the original experiment. If you wanted to purify a larger quantity of iodine, you could scale up and keep the proportion of reagents the same.
Scaling up the purification would actually be a chemical engineering project, so might require multiple experiments. Do complete the lab scale project first, and run your samples in duplicate if possible.
How are you going to measure the iodine?