When cold tranny not fully engaging

65 Dart Gt 225 with automatic. When I first start the car and try to drive it the tranny dos not engage fully. It seems to be slipping, no chatter or clunking. I have changed the fluid and filter with no change. Once it warms up (1mile) it works fine.
Is this common or do I have an issue that I can repair?

Note Johnny's post and try that to see if it works for you, but if it doesn't help that is known as "Morning Sickness" and is caused by hardened up rubber seals that don't seal until they get warm.
Heat makes them more pliable then it works good.
The solution is what is called a "Soft Parts Rebuild" as long as everything else is ok.
Also, a solution to having to put the trans in neutral to get fluid moving, or to check the fluid is an aftermarket manual valve that lets it circulate in park.
Then the fluid starts moving and filling the converter as soon as the motor starts.

I don't usually recommend this, but a leak stop product can help a morning sickness symptom as a temporary fix because these products work by softening the rubber parts.