Firstly I'm very surprised a UK doctor would be investigating or offering medication for fertility after just four months of TTC - most women who are able to conceive will do so within a year, so it is pertinent to wait that long until investigating and treating.
WRT to the holiday - how important is it to you that you go? If it pales into insignificance when compared with having a baby, then don't book. If you're not pregnant come April, you can always book then, safe in the knowledge you can still go and be safe to fly even if you were to conceive that day. If however, it's the holiday of a lifetime that you desperately want to be a part of, I would hold off TTC until April or so, so you're sure you won't book and then be stuffed.
I've flown short haul a few times while pregnant - all European destinations, mostly as I live on the continent but I also skied when in very early pregnancy with DD. I have a long haul flight booked in Feb (law of sod thoroughly invoked there!), for a family holiday to the caribbean. I have the insurance, I will get the 'fit to fly' note and will only be 22 weeks on holiday. I booked because I knew I'd be safe even if I did get pregnant (which I did, after a year of miscarriages and trying), and I know it is a relaxing holiday with family to help look after DD, food is high quality, water clean and healthcare good standard should I run into difficulties.