If I have type 1 diabetes, is it very likely that I will have to have a kidney transplant?

Not necessarily. It is estimated that it takes about 25 years of poorly controlled diabetes to cause cause renal failure. The will vary based on several factors including, age, diabetic control, other renal injuries or diseases (hypertension), etc.
Likely, but. It depends on how many years of diabetes you have. Kidney disease occurs usually after 12 to 15 years and starts mild and takes many years to need transplant. Also, technology is advancing fast and next 10 years things may well be different. If push comes to shove, remember to request a dual transplant for kidneys and pancreas. The latter will rid you of the diabetes.