Dear Wren,
Of course, if one believes in reincarnation, it is a possibility that your son may be your father come back to you. However, it may be prudent to not get too committed to proving that your son is your father reincarnated. I mean, you probably miss your father sorely, and wish that he were back in your life. A belief that your son is your father relieves the ache in your heart for him. The short interval between the death of your father and your son's birth may suggest that your father is NOT your son. Now, I know there are cases where people reportedly have reincarnated immediately after their death but if there really is another reality, more perfected than physical reality, into which we enter after the death of the body, then why would one want to leave it so quickly and return to earth. Unless your father had some strong desire to return to complete some unfinished business or had some obsession with physical life then I think it is unlikely that your son is your father reincarnated. But, of course neither I nor anyone else really knows.
Why don't you just let things unfold as they will. If it is for you to know that your son is your father then you will, in time, know it. He may give you clues to suggest that he has knowlegdge of your father's life. Undergoing a regression now may not be the thing for your to do, nor may it be in the best interest of your son. Your son is taking in your anxieties now about the death of your father and he may at a later date try accommodate you in your wish for your father's return. Perhaps it is in his best interest to let him have a new life, free of any spillover from a past life.
I definitely would not show him pictures of your dad now. Your son is only a little over a year old. He is taking in everything around him and showing him pictures to elicit some response is invalidating anything he may say in the future. Your interaction with him over your dad's pictures or other discussions of your dad's lifenow is not good.
In fact, I think that anything that your son may say in the future, perhaps, will be contaminated by your actions now and in the future. The validity of anything and everything he may say can easily be questioned due to his association with you at this early age and his discernment of your wishes for your father to return to you. From what you have written, I see no reason to believe that your son is your father returned to you. Unless he has said something relevant to past life recall, I think that it would be best for him,--- and for you too---to tuck this desire of yours in the back of your mind, and just wait to see what happens.
Please understand that I in no way want to be critical of your desire for your father's return and mean no offense, but it may be better if you deal with your own emotions surrounding the death of your father and try not to engage your little son in some fantasy wish fulfillment - Your friend, Wicker