How much would it cost to get a new battery?

Go to this web site for information about how to request battery service for your iPhone: iPhone Battery Repair & Replacement - Apple Support

For cost and availability, enter your model information in the "Get an estimate" box at the bottom. (I will let you do this since the answer will depend upon the country where you are located.)

Is it really time to change your battery? See this excerpt from the "Your battery's maximum capacity" section of the support article: iPhone Battery and Performance - Apple Support

"A normal battery is designed to retain up to 80% of its original capacity at 500 complete charge cycles when operating under normal conditions. The one-year warranty includes service coverage for a defective battery. If it is out of warranty, Apple offers battery service for a charge." In other words, if it is below 80% maximum capacity, it is below normal performance. You can still use it but you may wish to consider having it changed.

What location (i.e. country)?

You have options. If you're in the United States, it's now $89 plus tax directly from Apple, plus shipping if you choose to send it in. At an Apple Authorized Service Provider, the price can vary but tends to be close to the same price as Apple. The iPhone 11 series is not currently part of the self-service program, which starts with iPhone 12 models.

$89 U.S. at the Apple Store or authorized Apple Service shop.

You will need an appointment if you head to the Apple Store.