Catalyzes the GDP transfer from GTP to D-glycero-alpha-D-manno-heptose 1-phosphate, yielding GDP-D-alpha-D-heptose. Is able to use ATP, CTP or UTP as substrate in the presence of pyrophosphatase, but at a significantly slower rate. Can also form GDP-alpha-D-mannose from alpha-D-mannose 1-phosphate and GTP. D-glycero-alpha-D-manno-heptose 1-phosphate + GTP + H(+) = diphosphate + GDP-D-glycero-alpha-D-manno-heptose kcat is 3.0 sec(-1) and 1.35 sec(-1) for D-glycero-alpha-D-manno-heptose 1-phosphate determined by 31P NMR and HPLC method, respectively. Nucleotide-sugar biosynthesis; GDP-D-glycero-alpha-D-manno-heptose biosynthesis; GDP-D-glycero-alpha-D-manno-heptose from D-glycero-alpha-D-manno-heptose 7-phosphate: step 3/3. Capsule biogenesis; capsule polysaccharide biosynthesis. This enzyme is used in a preparative method to synthesize ample amount of GDP-D-glycero-alpha-D-manno-heptose to be used in elucidating biosynthetic pathways of various heptose components present in capsular polysaccharide (CPS) of C.jejuni. Belongs to the D-alpha-D-heptose-1-P guanylyltransferase family.