As pointed out, you've posted this in Backcountry Beginners forum and you neglected to give us any other clues about your experience level in mountaineering. I say mountaineering, not backpacking, because of you mention bringing ice axes, a rope, carabineers, and then speak of summiting peaks. Mountaineering requires very specific skills and often carries very high risks.

In the absence of any clear sense of your ability to safely carry out your plans, it's hard to do anything else but question how appropriate your plans are, rather than encourage you to undertake something well past your skill level.