Traveling while taking this med is totally doable once you sort a few things out. The medication itself is fine, just try to keep it cool (most hotels can help with that, or it's okay at room temp for almost a month if needed). Security allows it in your carry-on since it's a medical injection. The real trick is hydration, because GLP-1s reduce your thirst, and flying makes you dehydrated. You might feel awful if you're not constantly drinking water, even when you don't feel thirsty.
To help with electrolytes, I use these little unflavored drops that are easy to slip into a bag. Also, plan for an unpredictable appetite and bad food choices at airports. Pack some snacks (like protein) so you're not stuck with nothing. If you're crossing time zones, stick to your home schedule until you're settled, then adjust gradually. Most find travel is fine once they know what to expect.