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Under FED rules, the starting pitcher has to face at least one batter (until that batter's at-bat is complete) before he can be replaced. If the starting pitcher is unable to do so, he may not return as the pitcher for the duration of the game.
Other than that, there's no rule preventing pitcher and catcher from switching positions whenever they'd like (as long as none of the other substitution or re-entry rules are violated, which they aren't in your case).
I'm sure others will be around shortly to give insight into any other rulesets.
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