You can ask her nicely. You can call the police (non-emergency line). Or file a district court complaint for replevin (to return the dog) or depending on your "agreement" it seems like she breached a contract. So depending on more facts, you may have two theories to file suit on.
This is not legal advice nor does it create an attorney-client relationship. This is for education and informational purposes only. It is always recommended that you contact an attorney with any concerns as each individual case is unique.
Dogs, despite being adorable, are chattel. If your chattel is stolen, or wrongfully retained, call the police (do not attempt "self help"). Calling the police will initiate criminal proceedings, which will be handled by the State's Attorney, at no cost to you.
Alternatively, you can sue the person civilly for "replevin" (which is a fancy way of saying "give me my stuff back"). This process requires you to pay a filing fee, affect personal service on the defendant, hire an attorney, and plead your case to a judge.
Since lawsuits can destroy friendships, you should first try to resolve the situation in a way that does not involve the court system.
If you must involve the court, consider filing a replevin action in district court. In a replevin action, the court may order your friend to return your dog. Another option might be a detinue action. With detinue, the court may order your friend to pay you monetary damages (but you might not get the dog back).