Hi L.. Don't worry about all of these "suggestions" that you shouldn't "force" something. I completely understand why you want your LO to have a lovey. I'm surprised how opinionated people are on this matter! Who knew! Anyhow, my son needed something (a lovey) to help sooth himself at night because he WASN'T good at it and wouldn't take a paci. But either way, almost every book I've read on sleep says loveys are just fine and either kids give them up when they are ready or the lovey gets lost and that's that.
My son has the bunny version of your frog. He LOVES it and we actually bought two more, so we have three that we rotate around so that the one doesn't get totally worn out before it's time. He had a liking to it all on his own, but then I encouraged this bond by playing games with it (peek-a-boo, or just having the bunny give him kisses) and I would also let him hold on to it while he nursed. He is 9 months now and can sleep fine without it, but he does love it, and I love the smile he gets on his face when he sees it and holds it up to his face.
A note about blankets - my son, too, likes to put blankets on his face. He naps with a blanket and always did fine with it, so I tried it in his crib at night. He absolutely loved sleeping with it, but one night when I came in to feed him, it was wrapped around his head! Thank goodness he was ok, but I won't do that again (at least not until he's much older). You'll notice that the blanket part of the Bunnies By The Bay loveys (the brand that we have) is split in half so the blanket section isn't very big. I think that's intentional by the manufacturer so they can't suffocate themselves with it.
Anyhow... that's what we did. Good luck and have fun with your LO!