So, the difference in timeline of debt repayment would be less than 6 months????
In the long term, that really is practically irrelevant.
If you are planning to own, the math makes sense for you to own over renting, you have the money available to own, and the market is favourable, then yeah, buy a house. I seriously doubt that the interest on your debt over the next 4-5 months will add up to more than you would pay in principle payments on your new home, so you will probably end up ahead of the game in the end.
Unless you are living somewhere rent free at the moment, or looking to buy an overly expensive home...but that's another question entirely.