I'm thinking of resigning right away.

Literal

I [topic-は] immediately resign-volitional [quotative-と] thinking-am.

The volitional form 辞職しよう + と + 思う is the standard pattern for expressing 'thinking of doing / planning to do.' The volitional carries the nuance of commitment to the action; the かと inside softens it slightly to a tentative 'whether I should.' Here the か adds uncertainty — 'thinking about whether to resign.'