~UPDATE~ The surname of Katherine/Catherine is unknown. There is no proof that is was Killham or any varient of that name.
In England Mr. Whitehead in 1948 researched the birth, marriages, and of Dennington, parish.
From that information he was the first to show who the parents of Robert the immigrant were.
In 1960 Mr. Stanly Jarvis, also an English researcher there, researched the Dennington parish, but his report was about the same with only a few miner differences.
Neither of them found a marriage dt of Robert and Katherine. I then asked him to search the church warden accounts, town books, etc. of Dennington. He did not find any record of Robert & Katherine but several items were entered about the widow Elizabeth Goodale. One was that she took in boarders - something like an Inn.
Another item of interest was of a Prudent Artis: " Laide out for a paier of shoes for Prudent Artis - given to the widow Artis xiid and more if she was sick...Laide out to Gooddales wife and Nan Wallenger for helping Prudent Artis & mother Warbutton...1618 payed to Robert Goodale his wyef for helping Katherine Mitchell at 8d a week for 51 weeks , ended Easter 1619."
Mr Jarvis comments were: " It would seem to me that the Gooddale's wyfe mentioned as looking after Prudent Artis in 1617 is probably her relative Joan Artis who married Robert Goodale in 1590. Now it would appear that these two were helping a Katherine Mitchell. But this is the nearest I could get to any relation between a Robert Goodale and a Katherine.: /s/Stan Jarvis.
Now if you are searching mainly for the Killham lineage you might want to check the records in :Genalogical Gleanings in England" by Henry F. Watson Vol II. On page 1403 it has the will of Elizabeth Goodall and just below that is the will of Henry Killam of Dennington proved 3 Jun 1631. It continues on page 1404-5.
In regards to Ralph Kellam being the father of Katherine (Killham) it might be but it would not be the Katherine who m. Robert Godell.
There is no mention of a Ralph Killam in the Dennington parish, St Mary's parish included.
I greatly appreciate and thank Frank Goodell, father of Steve, for his helpful comments above.