Cellular respiration in carnivorous animals
Your guess is correct: glucose is not the sole source of energy in the cell!

While cellular respiration is the classic mechanism for energy production (in the form of ATP) in the cell, there's another process that's equally important and a little less well-known: beta oxidation. Beta oxidation is how fats and other lipids in the cell can be broken down to produce energy. In this process, the last two carbons in the long chain are sliced off and transferred to Acetyl-CoA, which can then be used in the citric acid cycle to produce ATP.

Here's the equation describing it:

$$C_{n}acyl-CoA+FAD+NAD^{+}+H_{2}O+CoA -&gt; C_{n-2}acyl-CoA+FADH_{2}+NADH+H^++acetylCoA$$

And here's a good diagram from the Wikipedia page that summarizes it:



Courtesy of Cruithne9 on Wikipedia [CC BY-SA 4.0 (https://creativecommons.org/licenses/by-sa/4.0)]

This process is why fats actually have a higher energy density than sugars: 9 Cal/g, as opposed to sugar's 4. It's also why organisms tend to use fats as energy storage - while sugar and cellular respiration is great for immediate energy, fats are stable and energy dense so it's an evolutionarily favored idea to use them for long-term storage.

You're also quite correct that animals don't tend to have a lot of free sugars and carbohydrates, unlike plants. Instead, we've converted those carbs into the fat molecules via the reverse process, fatty acid synthesis. So, carnivores largely get their energy from beta oxidation and the metabolism of fats, rather than glucose.