You can fly.
You can check from Turkish Airlines official web site;
I checked. On the 24th of May, you have 4 options to fly from Kayseri to Istanbul; there are 7 am, 10:55 am, 3.15 pm. or 8 pm flights. Then from Istanbul to Antalya you have 6 options at 9:30am, 11:25am, 2:25pm 5:30pm, 7:00pm or 11:55pm flights. The price changes from 101 YTL to 131 YTL if you buy right now. (1 British sterling is about 2,75 YTL) The sooner you buy, the less expensive it is going to be. There are also other airlines, (Onur, Atlas, Fly, Pegasus) but I dont think any of them fly directly from Kayseri to Antalya. You have to make a connection, therefore it is going to take half day. (4-7 hours depending on the time you have to wait in Istanbul)
Otherwise you'll have to rent a car. In that case it is about 600 kms. You can take in say 8-9 hours, and the second part of the road is a little bit dangereous, (the mountains and curvy roads etc) I dont advise that to you.
Have a nice trip.