"To fawn" (over someone/something) means to give excess attention to it, in order to please. I think you've chosen an appropriate verb. Interestingly, this dictionary definition uses a dog's behaviour as an example: http://www.thefreedictionary.com/fawning

Cuddly, cute, sweet, snuggle/snuggling. Fawn means a baby deer. Snuggling up to you.