Does a foreign child travelling within the USA need a passport?

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Crossing from Canada into the US by LAND :

Adults generally require a passport, although there are a few exceptions such as using a US or Canadian "Enhanced Drivers License" (which is a specific type of drivers license that includes citizenship details).
Children require either a passport, or a US or Canadian Birth Certificate.

So for this leg your child is fine, although you will require a passport.

Flying domestically within the US :

Adults generally require identification that meets the TSA standards. This includes both Canadian drivers licenses and well as passports.
Children under 18 years old do not require proof of identity. For an older child having something showing data of birth (to confirm they are under 18) may be helpful, but technically isn't required - and of course will not be required for a 2 year old.

So once again, your child is fine for this trip.

Returning to Canada by LAND :

The requirements are generally the same as entering the US from Canada by land. Technically an adult has the additional ability to use a birth certificate, but given a passport/EDL is required to enter the US this is largely a moot point.

Returning to Canada BY AIR :

You haven't mentioned how you are planning to return to Canada. Even for a child, a birth certificate is NOT sufficient to travel from the US to Canada by air - they require a passport. Technically once on Canadian soil a birth certificate would be sufficient to enter the country, however your child would generally not be allowed board the flight without a passport.

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Source: stackoverflow.com