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The January transfer window should bring no real changes to the Liverpool squad, I doubt any pivotal player would leave the team at the middle of such a great season.
However this does not indicate they would be undefeated throughout the season. There are still lots of matches left to be played and form can change in just a matter of weeks.
Yeah with the momentum Liverpool are having, I also don't think that anyone would want to leave such team. Also on other hand, Klopp is handing everyone a fair amount of chances and I haven't heard any player complaining as of now.
EPL is unpredictable... expect lot to happen in coming weeks.
Liverpool have a fixture againts Leicester on 27th December and two fixtures against Spurs and Man U in January. Apart from them, I don't find any major hurdles.