I've travelled all over with my DC. By the time dd was 2 she'd been to Africa (morocco, egypt, cape Verde), mexico, Thailand, Cuba, as well as all over Europe (Cyprus, France, Holland, Portugal, etc)
I'd say that avoiding the hottest places during their warmest times of year is a good idea, for my DC the optimum temperature is around 25celcius with a bit of leeway up or down but they don't enjoy scorching sun. Also, things are more expensive during the school holidays so enjoy cheaper prices whilst you can.
Have a look at villas and apartments as well as hotels. I prefer to have my own space, kitchen, private pool to being in a busy hotel with limited food options.
Always pack calpol and a digital thermometer as well as sunscreen. Make sure you have excellent travel insurance.
Expect your holidays to be different now you have DC. So if you normally spend your day lazing by the pool drinking cocktails realise you'll need to be sober, or if you love city breaks be aware that a toddler may not enjoy hours in a restaurant or museum...