My bike is a Scott CR1 weighs about 16-17 lbs, the front is compact 34/50 and the cassette is 12/26, my husband says its more than enough for the climb.
You might want to change out the cassette for a "MTB" 12/28 or 11/28 for this ride. The 28 teeth are beyond the usual spec for a road rear derailleur, but most seem to be able to reach. It'll give you a little bit easier gear for the hill climbing.