Find some of those orange/peach colored candy "peanuts" (I think they are supposed to be marshmallows or something) and decorate with them (put in pretty bowls). If no food allergies, you can put out real peanuts too. Find some, hopefully inexpensive, fabric with elephants on it and use as a tablecloth or runner and work with the other colors in the fabric. Check out www.orientaltrading.com or www.partycity.com, etc. for ideas/favors/decorations. Looks like they have an elephant pinata, make your own elephant ceramic banks (could be a great party "game" and then they could double as everyone's favors. You could do pink elephants or a zoo theme if you wanted a broader theme to work with. I'm betting you can find some elephant things under "circus" party decorations. There's probably a lot of Dumbo themed stuff that you might be able to use and/or play that movie in the background during the party. My son's 3rd birthday was a Toy Story 3 theme and I played that movie in the background and some kids that weren't into the games or who needed a break, plopped down and watched it. The invitations can say something like "Join us for ENORMOUS fun as we celebrate our Peanut turning 1!" Or you could go all out and do a fancy party and call it "Elegant Elephant." The elephant theme can really work for easy games for 1 year olds (since you can't plan/expect them to do too much). They could put up their arms by their mouths to make "trunks" and make elephant noises - best one wins a prize or something. Or just take cute photos of them to give to their parents later. Speaking of trunks, you could probably find little mini boxes that look like trunks and those could be party favor holders - you could do a lot with the "trunk" double entendre. Darn, I should have been a party planner - I'm getting excited about YOUR party! LOL! Anyhow, I think it will be an adorable party if you get creative and think outside of the box a little!
Don't forget to check out Etsy and/or Pinterest - they have EVERYTHING!!!