I own a Burley trailer, which I regularly attach to my De Rosa Planet and go for wonderful rides with my five year old daughter (who then yells to other riders that her daddy can pedal much faster than they can - introduces the anaerobic element to the ride! 🙄 ).
I would strongly advise you to avoid the 'kiddie bicycle seats', especially if you plan on doing more than riding around the block. The child sits very high up, and this completely destroys the balance on the bike (making steering and riding much less 'second nature' - not something you want when you are carrying your own flesh and blood on the ride). You are also exposing the child to far greater (IMHO) danger in case of a fall, as he/she is falling from a relatively great height. They get to stare at your back, and cannot play or take any toys along. And we have not even talked about the mounting hardware on a racing bike.
The bike trailers (there are a number of good producers, including several canadian firms as well as Burley and an excellent Danish trailer company) are quite safe (they are tubular alu usually, with a 'roll bar' and cross-chest safety belts and harness, so that even if you overturn the trailer they just hang there without bumping their heads), the child is comfortable (my daughter takes books, snacks, juice and assorted toys with her and regularly falls asleep during longer rides) and the mounting is done in minutes (I have the alternative hitch, which replaces the rear axle on the back hub).
The handling on your bike is not really affected, although it sucks the big one to ride up hill! I have gone on regular 20-30km rides with my daughter, and she loves it. We have even been caught in a rain storm, and with the waterproof carrier she loved the ride!
And you can find them relatively cheaply on ebay, of you are not willing to pay full price.
