It depends on how you created the paper wallet. If it has a private key QR-code, it could be as easy as installing
Coinomi, selecting Dogecoin, and Importing the key.
Depending on the amount (considering Dogecoin's rediculous value) you may want to use something more secure than an online Android phone, but that's up to you

Is there any risk to lose my coins in case transfer doesn't work? Or that maybe my coins will stuck in Coinomi wallet if asking my password?