Nothing wrong with going over mountains though I personally would leave at least 2000' between myself and the hills, if for nothing else to reduce turbulence. The other important factors are strange down drafts and giving yourself some insurance in case the unthinkable happens. I've experienced downdrafts in excess of 2000' / minute flying in the [too close to the....] mountains in the Western US which was quite frightening, I was wondering whether I was going to be able to climb before I hit the deck.
My view is do a flight plan if it gives you peace of mind, I wouldn't myself just becasue I think that it is more useful to let people [friends / family] know your route and ETA beforehand, and what to do if you don't arrive within say an hour. I carry a handheld ELT / handheld radio and mobile phone, so I feel pretty well covered if I were to FL.
Enjoy the flight though, mountain flying is wonderful, fantastic scenery...
Rgds
EA