Always tricky with those tourist visa's, however family visits do have pretty good success rates.
Historically the decision making has been quite fast usually just a couple of weeks.
Given that your sister will take only 3 weeks holiday with you, and given that the visa will be valid for 6 months, I'd be inclined to submit the application a little earlier. Just to allow plenty of time for planning etc and for any issues with UKBA
processing.
Recently, the full right of appeal for family visitor applicants has been removed. As yet there's no indication how this has affected the way in which ECO's now review such applications, if any.
That's the reason I suggest allowing extra time.
Traditionally there were very large numbers of family visit appeals in the 'system' and ECO's were required to 'double-check' all family visit applications falling for refusal to avoid issuing refusals that would be overturned at appeal.
Not trying to cause concern just informing you that changes have been made.
The cost of the visa is low at just £80
Your sister will be applying through Dubai, usually quick and positive outcomes.
Do some searches here to better understand the documentation you'll need to submit in support of the visit.