I am normally quite gung-ho about travelling, and would say if you were planning on backpacking in, say, Australia or Turkey or Spain or the US, yep, fine, you'd probably be able to cope.
I backpacked around Central America (OK about 15 years ago so a lot might have changed) for three months and it was one of the hardest places I've ever travelled in. We were doing it the hardcore way, but generally, comfort levels are low, it is hard to get food that is definitely not going to give you a dodgy tummy, bus journeys are long, uncomfortable, hot and crowded. Nearly everyone I met had had some kind of vomming/diarrhoea complaint at some point - it seemed pretty unavoidable, and of course that is not something to take lightly in early pregnancy. If you were trying to do any of it with the chronic exhaustion/morning sickness that are common features of the first trimester I would say there would be very little enjoyable about it!
HOWEVER you might be planning a totally different trip to the one I undertook. What you need to think about it: if I feel totally shit, and just need a day (or three) in a comfortable bed with bland, safe food, can I have that?
Booking-in appointment IMHO could happen prior to 8 weeks or after 14 weeks without being a biggy, but you would miss the window for your 12 week scan and the nuchal fold test, if that is important to you. There will be some healthcare where you are going, and some of it (depending on the country) will be quite good (Costa Rica for example has excellent medical care AFAIK). You can find health insurance that will cover you. Malaria is not a big risk in C America as far as I know so you could (as I did) take precautions instead of medication.
For me it would be weighing up whether, with your planned itinerary, you would have a decent shot of enjoying the trip. With my previous experience of C America, it wouldn't have been somewhere I'd have travelled at that stage. And actually, thinking about it, being away from home comforts for that long would not have been something I'd have really wanted to do feeling as I did in the first trimester. Backpacking at any time can be very tiring, however easy the destination - not having a base and some privacy for a long period of time wears you out.