No you will not need to extrapolate the cost over the year.  The amount entered for the deduction ($300) is proper. 

What is probably happening is when setting up the rental property in TurboTax you added some personal use days; probably 1/2 the year.  The personal use days are only days you personally used the property while it was a rental. 

Once the property became a rental, 1 Jul, for example, then there were probably no more personal use days.  Assuming you did not use the home yourself while it was a rental, you should enter zero personal use days.  

Revisit the "Rental" property topic.  Under the "Rental Type and Usage" section "Edit" the "Days Rented".  Blank out or "zero" the personal use days.   

Then when you enter the expenses they will not be reduced by any personal use days if that is the case.

Thank you very much!

If I enter personal days 0, how will turbotax handle insurance premium and mortgage interest? Do I need to manually calculate for 6mo period?

I always prefer to do the math myself in this situation where it is personal for part of the year. That way, you don't have to second guess any entries again.