You are absolutely right, it has a higher boiling point because it has more hydrogen bonds. However the bonds are slightly weaker since the oxygen are closer to each other and repel slightly more.
" The hydrogen bonds are slightly weaker (12–15%) than those in water " See https://www.google.com/amp/s/www.researchgate.net/publication/230086767_Hydrogen_bonding_in_hydrogen_peroxide_and_water_A_Raman_study_of_the_liquid_state/amp#ampshare=https://www.researchgate.net/publication/230086767_Hydrogen_bonding_in_hydrogen_peroxide_and_water_A_Raman_study_of_the_liquid_state
Edit my appologies, maxW was earlier with approximate the same answer but I did not see his comment. Should I delete this awnser so you can get the credits you deserve? (Glad to know we are on the same page :)