Yes, this is quite common and is perfectly safe and legal to do so. While not always required when travelling within Ireland and the UK with IVF injections, a doctor's letter is highly recommended. This document should state:
As long as you have a letter, there is no issue with carrying your medication in your hand luggage. Thérapie Fertility can provide a letter for you to show your airline if necessary.
We would recommend that you wait to travel until the day following your Egg Collection.
Yes, it is perfectly safe to travel on the same day as your embryo transfer, if that is what suits you the best.
Most IVF injections must be kept refrigerated between 2-8°C. You can ensure your meds are kept at the correct temperature while on the move by using a simple chilled food storage bag.
As with any international travel, it is generally a good idea to have travel insurance in place before your trip. Not all travel insurance policies cover IVF treatments, so make sure to read the small print. If required, specialist insurance for fertility treatment travel exists - Look for policies that explicitly cover IVF treatment or pregnancy.
In order to reduce the need for travel during ovarian stimulation (or stims) we have a satellite clinic in London. You may attend this clinic for all of your ultrasounds throughout ovarian stimulation, travelling to Dublin only for the actual Egg Collection procedure.