Can a celebrant perform a marriage of his own son or daughter?

Yes, well Civil Celebrants can, so I imagine it depends on the particular Religion for Religious Celebrants.

yes perfectly legal 

Yes, as long as all legal requirements are met. I have married many family members and would love to marry one of my children should I get the opportunity.

absolutely yes, many celebrants only get the qualification to marry their family

Yes, there is nothing stopping either a civil or religious celebrant to perform the wedding of a their child, provided all other legalities are complied with. 

I had a chat with my daughter, who is 12 years old, just yesterday about this very thing, I said to her that I wouldn't be able to walk her down the aisle unless I do and then promptly take my position as celebrant. Perhaps her brother could walk her down the aisle. Be a lot easier to do the ceremony for a son as it would be harder to give up the traditional role of walking your daughter down the aisle. No probs for a female celebrant though.

Anyway, it would be an honour to do the wedding of a child. 

All the best!

As a Celebrant we can and I have officiated wedding ceremonies for my son and daughter.

It is such a special feeling when it is your own child, not that every wedding is special to me.

As for a religious minister, I'm not sure but don't see why not

Hope this is helpful and have a wonderful day.

There is nothing stopping you as a Civil Celebrant to marry your own children, siblings,relatives.I have married my nephew and niece to their partners and I found it to be such a special day not only for them but also for me as I felt so honoured knowing I am their Uncle that i married them.It's a more relaxed atmosphere as you know everyone present  as they are family.

Yes an authorised celebrant can legally perform weddings for anyone who wishes to marry and this includes any of their family members - including their own children.