Welcome back to the CCF. Yes, it is exciting to find "in the wild" a shiny old penny, but please realise not every old coin in good condition is worth buckets of money. Being new to the hobby, the best investment is in good reference materials, such as the
Red Book of U.S. Coins. Also, when presenting photos to us it is best to take coins out of plastic.
What makes you believe your cent was minted on a dime planchet? A 1963 cent if minted on a dime planchet would be silver, not copper and would be the same size and weight as a dime, is yours? Also, since dimes are physically smaller, your penny would look distorted and would appear to wrap around the coin... looking at yours, it has well defined rims, so this isn't the case. So, no dime planchet I'm afraid.
Should you have it graded? Well, of course that's up to you, but in general, the "rule of thumb" is that after taking in account the grading fees (which aren't cheap), your graded coin should be valued at least $150. Looking up values, a 1963 cent in Mint State (which your is not, but its hard to see because we're seeing it behind plastic), the value would be $12 to $15 roughly. So with the cheapest grading, you aren't even half way to the $150 benchmark.
So, I hope this helps to answer your questions. We get a LOT of new people asking/thinking their coin has to be worth big bucks, and unfortunately, the answer is no, they are not. Very very rarely, yes, but in cases such as yours, I am sorry, while a neat find, its not a valuable coin. But keep it, build a collection around it, and have fun. As I suggested, good reference materials really help, and by all means, continue to ask questions here. We are here to help!
