I'm a male with O positive blood type. My girlfriend has AB positive blood type.
Are we medically compatible? Do we have good odds of having healthy offspring? Is there anything we should be aware of during pregnancy?
This is something to be confirmed by your doctor and I'm not sure why you're worried, but
ABO blood group incompatibilities between the mother and child does not usually cause hemolytic disease of the newborn (HDN) because antibodies to the ABO blood groups are usually of the IgM type, which do not cross the placenta. However, in an O-type mother, IgG ABO antibodies are produced and the baby can potentially develop ABO hemolytic disease of the newborn.
https://en.wikipedia.org/wiki/ABO_blood_group_system#ABO_hemolytic_disease_of_the_newborn
This means that you being O and her being AB is not an issue in terms of conceiving or carrying a baby.
You are both "positive" on Rh factor.
The hemolytic condition occurs when there is an incompatibility between the blood types of the mother and the fetus. There is also potential incompatibility if the mother is Rh negative and the father is positive. When any incompatibility is detected, the mother often receives an injection at 28 weeks gestation and at birth to avoid the development of antibodies toward the fetus.
https://en.wikipedia.org/wiki/Rh_blood_group_system#Hemolytic_disease_of_the_newborn
You don't have a combination known to cause trouble, and if you did, there are treatments during pregnancy to prevent the trouble.
Why are you worried you might not be "medically compatible"? There doesn't seem to be any evidence that you are not.