Yeah, it does look funny when you look at it for awhile. I was told that you should include the period within the quotation marks, but I'm not the punctuation police.
I tried that and it looked weird that way too. I went back and forth a couple of times and stared at it, and it looked funny both ways. I even thought of not having any period there at all. I just couldn't win!
I think my brain shut off about 4 hours ago.