Do Latter-day Saints believe that they will “get their own planet”?
No. This idea is not taught in Latter-day Saint scripture, nor is it a doctrine of the Church. This misunderstanding stems from speculative comments unreflective of scriptural doctrine. Latter-day Saints believe that we are all sons and daughters of God and that all of us have the potential to grow during and after this life to become like our Heavenly Father (see Romans 8:16-17). The Church does not and has never purported to fully understand the specifics of Christ’s statement that “in my Father’s house are many mansions” (John 14:2).Frequently Asked Questions, Question 12: https://newsroom.churchofjesuschrist.org/article/frequently-asked-questions & https://www.churchofjesuschrist.org/study/liahona/2010/10/commonly-asked-questions?lang=eng
While against the backdrop of infinite creation we may appear to be nothing, we have a spark of eternal fire burning within our breast. We have the incomprehensible promise of exaltation—worlds without end—within our grasp. And it is God’s great desire to help us reach it.Dieter F. Uchtdorf, Second Counselor in the First Presidency, October 2011 General Conference talk “You Matter to Him” https://www.churchofjesuschrist.org/study/general-conference/2011/10/you-matter-to-him?lang=eng