I want to convert a half bath into full bath

This iis a major remodel. First you will have to purchase a shower base and enclosure that will fit into the half bath. Is the half bath on a cement slab or a wooden floor? Will you be doing the work yourself? Back to you!

Unfortunately, whenever you are talking about renovations, both kitchens and baths rank among the top for cost. However typically upgrading these two areas can also pay dividends on resale in a "good" housing market.

That are a lot of variables that were left out of your question, so it's hard to say...however I will be as general as I can.

Most Cost Effective
In order for your quick fix to be cost effective, you will need space in the half bath to install a shower stall. A 34"x34" stall would be a min. Size you would want.

Going to Cost a Little More
If you don't have space in the bathroom, check to see if there is an adjoining closet that you can utilize or steal space from (at least 36" clear), however you will need to confirm dims with the shower base you obtain for clearances. The smallest unit you want to go with is 34"x34" (again for resale value). Be careful not to take away closet space from a bedroom, as that will reduce resale $$.

Are you willing to spend?
If you don't have any space adjacent to grab, you will need to rework the whole area. This is where most homeowners make the biggest mistake. They try to rework the whole area themselves thinking that it would save them money, however you should get a qualified architect/space planner to really get the biggest bang for your $$$. The cost difference between hiring an architect vs just placing rooms where they fit can have a HUGE impact the return of $$$ for resale.

Don't forget, you will need to get permits for the plumbing work, especially since you are planning to sell.

Hope this adds some insight...

Considering you plan to sell in a few months I would not even start the project but that's just me. Unless you find that spare space somewhere this full bath will be so tight that home buyers will not like what you did. This is not considered a full bath if you go with a shower, realators would call it a 3/4 bath I believe.