Reaction of hydrogen peroxide with sodium carbonate
The impossibility of a reaction producing simultaneously $\ce{Na_2O_2, H_2O_2}$ and $\ce{CO_2}$ can be proved by the following arguments, drawn from the Merck Index, under the reference "$8728$. Sodium Peroxide". 

1) $\ce{Na_2O_2}$ is produced by burning metallic sodium in a current of air, from which carbon dioxide has been removed. 

2) $\ce{Na_2O_2}$ reacts so easily with $\ce{CO_2}$ that it is used for rendering air charged with $\ce{CO_2}$ respirable as in submarines and diving bells.

3) $\ce{Na_2O_2}$ absorbs water from the air forming sodium hydroxyde and hydrogen peroxide, the latter quickly decomposed into Oxygen and water. 

Ref.: Maryadele O'Neil, Ann Smith, et al., The Merck Index, An Encyclopedia of Chemicals, 13th Ed. 2001, Merck &amp; Co Inc., Whitehouse Station, NJ, USA.