too tired to... or too tired for...
"too tired to" + verb
"too tired for" + noun. "Walking" in your example is a gerund, which is the noun form of a verb -- the act of walking.
"too tired to walk" and "too tired for walking" mean pretty much the same thing, and either would fit in the dialog above. The second for, "..for walking" may be a bit more general, but it is clear from the context that it applies to the immediate situation.