SpaceX will not build a new nosecone for the Starhopper. Elon Musk tweeted that the new nosecone is being built for the orbital Starship.
Elon has previously indicated that the orbital version of the Starship would be completed in June 2019. Elon Musk has tweeted that the first orbital Starship upper stage prototype should be completed by June 2019. He has stated that the Super Heavy first stage will start construction in the spring. If the Starhopper has successful testing from April through June, then an orbital test could happen in the latter half of 2019. SpaceX will be able to build the 38 Raptor engines for a full Super Heavy Starship. SpaceX has completed full testing of the stainless steel heat shield tiles. The SpaceX Falcon Heavy succeed on its first launch into space. The Falcon Heavy had 27 engines. The engines were similar in size to the Raptor engines. SpaceX has landed many first stages. The Starship is seven engines and following the same development plan. If the first launch success of the Falcon Heavy was not a fluke, then SpaceX could have made breakthroughs in computational design and pre-orbital testing.