I've gathered from an earlier question that Gryffindor probably played the final game of the season during Philosopher's Stone with six players. Amflare found this helpful quote:

"Now, listen here, you lot," [Wood] said, glowering at them all, "we should have won the Quidditch Cup last year. We’re easily the best team. But unfortunately, owing to circumstances beyond our control..."
Harry shifted guiltily in his seat. He had been unconscious in the hospital wing for the final match of the previous year, meaning that Gryffindor had been a player short and had suffered their worst defeat in three hundred years.
_{(Chamber of Secrets, Chapter 7, Mudbloods and Murmurs).}

Wood's response when Professor McGonagall introduces Harry to him also heavily suggests that at that point Gryffindor had no Seeker at all.

"Potter, this is Oliver Wood. Wood - I've found you a Seeker."
Wood's expression changed from puzzlement to delight.
"Are you serious, Professor?"
_{(Philosopher's Stone, Chapter 9, The Midnight Duel).}

McGonagall surely wouldn't have bothered to show Harry to Wood if Gryffindor already had a Seeker in place, even if Harry was uncommonly good. Common courtesy would demand that that Seeker should be given at least a game in which to prove themselves before Harry was given a chance. Furthermore, Wood is delighted and disbelieving when McGonagall tells him that she has uncovered a Seeker. Not a good Seeker (she hasn't told him how talented Harry is yet), just a Seeker. All of this suggests that Wood was totally desperate because he hadn't appointed a Seeker and that Harry was the answer to his prayers.

Am I correct in this assessment? If I am then why did Gryffindor not have a Seeker already?

Players are appointed through trials at the start of the year. Wood had two vacancies to fill: Seeker and Chaser. We know that he appointed Katie Bell at the trials that year - since she and Harry are in the same year and she had already been appointed by the time Harry joined the team. If Wood appointed Bell through the trials why didn't he also appoint a Seeker? It's the most important position on the team, after all. A team without a Seeker may as well not bother turning up. We know that Wood was replacing a very talented Seeker in Charlie Weasley so his standards were probably quite high. But surely any captain would prefer to have a poor/average Seeker than no Seeker at all?

Why didn't Gryffidor already have a Seeker in place by the time Harry joined the team?