Formation of Goethite
TL;DR  Yes, the reaction is feasible at $\pu{60 ^\circ C}$. Just extending my comment into an answer.

Goethite and ferrihydrite(not ferrihydrate) are two different things. They are polymorphs of iron oxyhydroxide ($\ce{FeOOH}$). Goethite is $\ce{α-FeO(OH)}$ while ferrihydrite is amorphous/nanocrystalline hydrated iron oxide, officially formulated as $\ce{FeOOH•1.8H2O}$ but also exist in many hydrated states and so formula is theoretically indeterminate as its water content is variable.

Reaction between iron(III) nitrate hydrate in alkaline solution has been studied by Atkinson et al.1 at different concentrations and amounts. One case is: 50g of $\ce{Fe(NO3)3}$ salt dissolved in 825 ml of water is added to $\ce{200 ml 2.5 N}$ potassium hydroxide solution. At pH 12 and maintaining the temperature at $\pu{60 ^\circ C}$, it took 24 hours to complete the reaction. They also noted that in this goethite synthesis, ferrihydrite is the initial precipitate that results from the rapid hydrolysis of Fe(III) solutions, before aging to goethite at higher temperature.
Pure ferrihydrite synthesis is difficult to isolate because it requires careful control of pH and temperature and its composition can changes if any of this parameter changes. Also, ferrihydrite is the only polymorph which is called nanomineral because its crystal size is in the range of 2 nm to 5nm. Nonetheless, its synthesis has also been discussed in the same paper where ferric nitrate is dissolved in potassium hydroxide but the pH is maintained at 7-8. Vigorous stirring and centrifugation yields the ferrihydrite.
An alternative reaction where the pH is not needed to maintain strictly is by adding $\ce{Fe(NO3)3.9H2O}$ and $\ce{NH4HCO3}$ in a 1:3 mole ratio at $\pu{80-100 °C}$ 2 or iron(II) salt or iron(III) salt with silicon or germanium at pH 5-11 3.
Notes and References

Laboratory synthesis of goethite and ferrihydrite of controlled particle sizes by
Milton Villacís-García, Mariana Ugalde-Arzate, Katherine Vaca-Escobar, Mario Villalobos,
Rodolfo Zanella, Nadia Martínez-Villegas, Boletín de la Sociedad Geológica Mexicana
Volumen 67, núm. 3, 2015, p. 433-446 (PDF)
Novel Synthesis and Structural Analysis of Ferrihydrite
Stacey J. Smith, Katharine Page, Hyunjeong Kim, Branton J. Campbell, Juliana Boerio-Goates, and Brian F. Woodfield
Inorganic Chemistry, 2012 51 (11), 6421-6424
DOI: 10.1021/ic300937f
SYNTHESIS OF FERRIHYDRITE AND FEROXYHYTE, NAGANORI YOSHINAGA and NOBORU KANASAKI
Faculty of Agriculture, Ehime University, Matsuyama 790, Japan, Clay Science 9, 43-51 (1993), (PDF)
Simple hydrolysis of iron(III) nitrate yields $\ce{\alpha-Fe2O3}$. Fusion of potassium hydroxide and iron(III) oxide ($\ce{Fe2O3}$) in air produces potassium(VI) ferrate but in laboratory, $\ce{K2FeO4}$ is prepared by oxidizing an alkaline solution of an iron(III) salt with concentrated chlorine bleach.